It kind of goes without saying, but in a lot of cases it really depends on where you're travelling from. Making points like "it's far away" doesn't really indicate general difficulty. Far way from what? Your house? So what? A train station? Fair point.
Some of the examples above I found very simple, while I'm sure some of my "difficult" ones will have been done more easily by others. I'll list a few that I found generally to be a faff. This is by public transport. I've found that most parks are accessible this way, even in the US, but some are very time-consuming with few options.
China's a tough one since I tend to take a Taxi/Didi everywhere unless it's right near a metro station. Public transport in China is excellent, and even the difficult parks are generally accessible by bus, but buses are really not very foreigner friendly (no English signage, timetables etc.), The "faff" element of those, for me, would be more to do with taxi availability and taxi drivers' knowledge. Some of them seem unfamiliar even with the bigger parks, so the smaller cred-run places can be very tough. Now though, using Didi (Chinese Uber) totally takes that barrier away, and I wouldn't really consider anywhere in China to be an issue now that that exists..
Anyway, parks I have had faff with before, beyond just "it was far in a taxi" or drivers not knowing where something was:
Chuanlord Holiday Manor
I've been twice. The first time was a big faff, the 2nd time less so and I imagine any future visit will be fine. Getting to the place by taxi was fine though I seem to remember probably having to try a couple of different drivers, but getting out was awful. The first time, I either didn't notice (or it wasn't there at that time) the group of bus stops. There were no taxis around, so I walked to the main road. There were no taxis there either since it's right next to a toll booth and no drivers are going to be hitting that without a passenger. I found a bus stop and just got on the first bus which came, having no idea where it was going, but getting off when we hit a more built up area and finding a taxi there. On the 2nd visit, I seem to remember getting on a bus outside the park, but jumping off and into a taxi when one pulled in. These days: Didi = easy. It's also not that far away from a train station, but I didn't know that at the time.
Locajoy Holiday Park
This place was really far from the city (Chongqing) and I couldn't find any viable public transport options at the time. It was also a 90-minute drive, so a taxi wasn't really an option as I doubted they would accept the fare (even if they knew where it was). I ended up booking a limo and driver for the day through the hotel.
Long Gu Wan Dinosaur Park
Actually very close to the main highway between the airport and Nanning city centre, but apparently no easy way to access it. I used Didi to get there, but the app took a weird route down a muddy track through some fields, making it feel more "in the middle of nowhere" than it actually was. The faff for me was getting out since I had (for the first and last time) a problem with Didi. The payment for the outgoing ride hadn't gone through, so I couldn't book another Didi car. I had to go to guest services for them to call a taxi, which took an hour to arrive. The Didi thing, obviously, sorted itself out right as I was getting in the taxi.
Fantawild Asian Legends
Part of the same weekend as the above park, which was my back-up park when Fantawild didn't happen. The park itself is not a faff at all. It's well located and easy to get to by taxi. However, on the day I wanted to go, there was a marathon. From my hotel, I needed to cross the river to get to the park, but all the bridges were closed off. I spent about an hour in the taxi, driving along the river to a bunch of different bridges, which were all closed. I went back the next day with no issues, though.
There are a bunch of other small, pain-in-the-arse parks, but they were down to distance and/or taxi driver stupidity, so I won't go into them (can't remember details either to be honest; I'm sure there are rants in the relevant trip reports). Plus, like I said, using Didi takes away 99% of those previous issues. Some others that spring to mind then:
Valleyfair
This place is possible by public transport from Minneapolis, but you only really have one option to get there and one to get back. First, it's a bus (only runs once in the morning) to some little "transport centre" (shed) outside the city. Then, there's a small local minibus to a bus stop next to nothing, from where it's a 15-20 minute walk to the park. It's then the same in reverse to get back, only it's then that you realise the bus stop isn't even marked; it's just a bench next the road, so you spend the 15 minutes while the bus is running late panicking that you're at the wrong place and you won't get back to the city. It was the right place, and they held up the connecting bus so people could make it, but still. Total faff.
Michigan's Adventure
There is a bus that runs between Muskegon and the park, but only on weekdays, which seems stupid for an amusement park, but there it is. Taxi it is then. This was also a huge faff in general since in order to do the park at all - as in getting into and out of Muskegon itself - it meant a very long bus ride (from Chicago) and a two-night stay. Stupidity on my part really, but creds.
Otherwise, I don't think I've had any big issues with American parks. Sure, driving would be much, much, much better in the vast majority of cases, and there's planning involved since the frequency can be low, but the public transport options do exist in some form for the most part. There are very few I would label as "good" though. It usually means some early mornings and either getting back late or leaving parks well before closing time. Having said that, I did just opt for Uber for Six Flags Over Texas and the two San Antonio parks, the latter of which seemed to have buses, but I couldn't be bothered. It has also meant longer stays in some areas since there's no way out until the next day etc. Also, forget any ideas of hitting multiple parks in one day; not going to happen. Long story short: it's all very possible, but a pain in the arse.
Adlabs Imagica
There is park/shuttle bus option, but it's impossible to book it with a foreign credit card. Plus, the location of the bus stop isn't explained clearly and seems to be a pain in itself depending on where you're staying. I think they may have moved this bus stop to the main train station now though. The other option, a slow train from the main station in Mumbai followed by tuk-tuk is certainly an experience, though not really difficult.
Legoland Malaysia
Despite being in Malaysia, a lot of people do this from Singapore, so it requires a border crossing. There's an official bus that goes to and from Singapore, so it's easy, but you're stuck for the whole day. Legoland Florida has the same issue.
Alton Towers
No need to comment further, but it's just stupid for a park of that size and popularity.
Bayern Park
Only one bus in and one back out when I was there, meaning a whole day at a place without a huge amount to do.
Plohn
A train from Leipzig to Zwickau to connect to an irregular bus to somewhere nearby the park. This is followed by a longish walk from the bus stop, and an even longer walk when leaving later to a nearby town for a tram , again back to Zwickau, thanks to the aforementioned bus not running very often. Also, NONE of this information (bus times/numbers etc.) comes up through Google Maps, making it seem like public transport isn't an option. It is; it's just a PITA.
Skyline Park
A walk through a field after getting off a very irregular train at one of those stations that is little more than a glorified bus stop.
Other than those, I don't think I've had any real issues with European parks. Europa needs something better, but it's not bad. Drievliet was confusing (tram stop and then a walk through an industrial estate), but the trams are really frequent at least. I think Duinrell needed a couple of buses with a random transfer on some residential street, but the drivers were all really helpful.
Japan
A few parks fit into a similar category: relatively good transport, but can take a long time and require train-bus connections. Off the top of my head: Mitsui Greenland (not difficult, but takes a while), Hamanako Pal Pal (long bus ride to/from the nearest train station), Lagunasia (quite a long walk to/from the bus), Kijima Kogen (infrequent buses), Parque Espana (ended up taking a very expensive taxi from the nearest train station).
Taiwan
All the parks require buses from the nearby cities. I'm sure it's easier now, but when I went (2007?), it was quite difficult to get information, even from tourist information offices. These buses also only seemed to run once or twice a day in each direction. As I said, it was a long time ago now, and pre-smart phone, so I imagine it's a lot less stressful these days.
Christ, that post's long enough now.