I might stick my head out with a provocative opinion and say that the CART/IRL split is actually quite a fitting comparison - and ironically might have helped US open wheel series to come back, while F1 is still in free fall. Let me explain:
Yes, CART was probably the absolute height of US open wheel racing, but so was nearly any series in the world at that time. F1, touring cars (BTCC, DTM, etc.), maybe except for sportscars, who had been killed off by Bernie on purpose, were experiencing their golden eras.
But none of those series was able to maintain that level. The reason is that the mid-1990s were also the height of money influx into motorsports. TV channels pumped money into it, new countries wanted to host races, tobacco sponsors were crazy for racing series. This resulted in the 1990s being the peak of most series, and like all bubbles, the motorsports bubble burst as well. Not only F1, but also touring cars (ITC) and US open wheel scene were suffering from unsustainable costs, so those series have been in a fall since then (at least until, with 15 or so years of lag, people in those series realised that the golden years were over and you need to keep racing affordable). Probably sportscars are the only series that benefitted after the mid-1990s, because it gave a good bang for the buck: Audi, Peugot, Toyota, they all went to Le Mans because it was a big race that you could do on a comparatively small budget.
What I want to say is that the CART/IRL split was not the cause of US open wheelers going downhill, but the first symptom, some form of hybris by all participants involved (not unlike the ITC, which killed the DTM).
F1 was lucky not to split, but this came at the HUGE price of buying teams like Ferrari for even more money that nobody can really say why they should get it. So while CART broke apart and had to suffer through 20 bad years, because they could not arrange to stay together, F1 has been going downhill because the arrangement that was made to keep the series together only amplified the imbalances within the sport (i.e., biggest teams/manufacturers have been co-opted at the expense of the small teams).
Both F1 and CART had different paths, but the underlying problems were similar (who gets the biggest stake of the huge influx of money? MONEY!).
But because CART/IRL was so blatantly hurting the sport, the crash came quicker. And although it hurt, the resulting IndyCar series is probably my favourite series right now. Yes, it's basically a spec series. Yes, it has lost some of its iconic teams and tracks, and yes it is building up from way down there, with only a fraction of the fans/viewers. But at least they got it done, and the package is getting better. At most important of all: I think they are rebuilding it in a more sustainable way. Sure, IndyCar will have crises in the future (like every business), but the platform seems built on a stronger foundation.
F1's problems, on the other hand, were just hidden and postponed (maybe hoping for another 'gold rush' by big sponsors, which everybody should have known would never come). The foundation not only is more shaky, it really seems like an inverted pyramid, with everybody on top trying to balance things out, although everybody is aware that it will topple over soon (for example, if the small teams close, because then the sport will get more expensive for the big teams as well, keyword "3-car-teams", and the big manufacturers will be forced to leave by their shareholders).
The split was averted for F1, but the underlying issues were not fixed. They just got a decade and a half further, and now the structural problems are resurfacing. There won't be a split, because nobody can afford a split anymore. It will be much worse: we'll just lose half of the grid over the next couple of years.
So in some way I wish F1 had split. Then at least we'd have some puzzle pieces on which we could construct a future. But when we lose Sauber, Force India or even Williams, there won't be a lot to save.