There’s two things going on there though - one is a p will sit in a mix a lot easier - so without much eq on the recording will probably sound nicer.
the second is if you’ve been chasing the idea of the bass you want rather than the sound. A few years ago I had 100% active thru necks, my main bass with a cool ACG preamp. All good till I took a punt on a bass I had been recommended “buy if you find one” by a flat mate years ago. Roll forward 2 years and most my basses are bolt on basses with a fender type sound. Maybe the idea of the stunning graphite and sparkle finish flea bass is better than the actual sounds you want to make with it