I wouldn't call it a "limit" but more a matter of efficiency and practicality. You could put in a ton of work to develop those fast chops on your thumpy P-bass, or you could set up another bass in a way that makes those fast techniques a lot easier to reach.
Just like you COULD ride your bicycle across town instead of driving. One method just takes a lot more work.
Personally, my approach is to make the instrument as easy to play as possible with the assumption that if it plays effortlessly I can always dial in good tone to match feeling good, but a big fat tone doesn't do any good if I play poorly because I am fighting the bass itself.
If it's feasible I'd suggest either taking one of your basses or picking up a cheap one and trying to set it up specifically for technical stuff and fast playing. Get something with a thin neck, a lot of frets, and slap super light strings on or even try tuning it E-C (5 string) or A-C (4 string.) It might not be the bass you play all night with the band, but it could be a tool to woodshed techniques, transcribe solos, and dial in faster stuff that you can then shift over to your other basses once it feels comfortable on the easy one.
And just in case you don't do it already, crank the volume way up and play with the lightest touch possible. If you are used to thumping hard on big strings then light strings with a light touch will open up all sorts of technical possibilities. Let your amp do the work for you so your effort is only to make the strings vibrate, not to produce gain.
