^^I think the ride type will survive just fine.
Swinging ships were never meant to be centerpiece attractions. They're a kind of filler attraction, one that gives the crowds something to do in your park after being drawn in by the bigger, more spectacular rides. The non-inverting kind is a bit of a "stepping stone" ride for younger audiences too. They also don't use vast amounts of land or cost a fortune. It's the kind of ride you build in a low-investment season, possibly to revitalize some little corner of the park.
Still, it is a "big, mechanical ride" of the type most people don't see every day - or every year, for that matter. As enthusiasts, we're likely to skip rides like that, but other people on their biennial theme park visit might find it thrilling enough to bother to queue for. They'll see it as yet another fun, out-of-the-ordinary type of attraction. Another element in their fun day at a park. A swinging ship, much like most other types of rides, is good enough to satisfy people already in the park, but they probably won't ever be the main reason for people to go there.