Those reggae greats chose the Jazz bass for a good reason. The neck pickup is closer to the fretboard and thus "fatter" and "warmer" than the P bass with its pickup more centrally located between the end of the fingerboard and the bridge. The classic reggae tone is Jazz bass with neck pickup 100 % and bridge pickup probably nil. I've seen some reggae players use a Hofner-type violin bass which also features a neck pickup. The P bass has too much low-mids for a good reggae sound. IMHO.
I suppose you're right. But I don't think I can get over my Pbass compulsion