Some strings, not all, might break or unravel if you either cut them too short or wind the full diameter of the string on the tuners. It's much more likely to cause breakage on flatwound strings. Rounds might be OK.
The other problem is that you can only cut the string so short and the full diameter of a B or E string is not going to fit through the slot on the tuner, so you need to leave a little bit of the tapered segment of the end to fit into the slot and down the little hole. So then you're left winding a bunch of fat string on the tuning peg, and you'll be more likely to run into problems if the string starts to overlap itself.
Even with strings that fit a particular bass, you don't want to overlap the strings on the tuner because it can cause slippage that can make it hard to keep the bass in tune.
EDIT: This is speaking only from my own experiences. I'm sure some crusty old diehard will jump in and say they've been using .145 strings on a 25" scale bass with 15 wraps around the tuners for 33 years and never had a problem.