I have a spin bike. Not all of them will take real bicycle seats and pedals. If you get one that doesn't you will be stuck with an uncomfortable fat-ass seat and lousy pedals.
Even with real seat and pedals, it's not that much fun. I don't like fixed gear- I keep forgetting and try to stop pedalling like I do on a road bike. I may be able to fit a freewheel to mine. And the fit is not the same, as pointed out earlier.
OTOH, vs putting a bike on a trainer- I can just go use the spin bike. I don't need to set up the trainer, then get a bike from the garage and mount it on the trainer.