There's the obvious thing, less to go wrong. Not having moving switch parts makes the probe simpler and thus more reliable. Also good high frequency switches are surprisingly hard to make and the switches in switchable probes aren't always the best.
Then, there's the "left it on the wrong setting" and, more often, "didn't realise I'd accidentally put it on 1x" problem with switchable probes - you'd be surprised how often this happens in practice, and how much time you can waste chasing down a "circuit" problem only to realise too late that a wrong probe setting was the problem.
Finally, any switchable probe is going to compromise between the best settings/compensation for 10x and the best settings/compensation for 1x. That's an inevitable consequence of making one thing to do two tasks, it can't be optimised to do both.
For the most part using switchable probes isn't an issue for most people making most measurements. You're more likely to accrue measurement errors from loading, probing technique and the general laxness of oscilloscope specifications (3% voltage accuracy on a lot of scopes) than from the weaknesses of switchable probes. Once you get into the territory above 100MHz (roughly) then probe infidelities become more important. Using switchable probes at 500 MHz would not be a good idea and, apart from the odd maverick Chinese OEM, nobody makes switchable probes for those kind of frequency ranges for exactly that reason.