With the P and J shape being so ubiquitous I just think they are what pop into my head when people say bass. Like if you say hatchback car I would think VW Golf and Estate probably a Volvo. Neither offensive or exciting just nicely car shaped!
When it comes to the sound of a P or J, well othat’s a different matter. If I was looking for a P bass sound I may as well get a P bass.
Edit: The exception to this for me is the Jazz. The looks neither excite nor bore me. It’s a classic shape that is pleasing on the eye, but I have had a couple and find the shape a bit annoying in use. Tempted to sell the one I have now and get a Sandberg J.