I think a P with flats is fabulous in a recording environment, largely bc the mixing can make it poke out sufficiently, and the engineer can drop the levels of other instruments and eq everything to “play nice”. Think old Stax and most any 45 rpm record.
It is also great to play on stage, but I have much less success in a live environment being heard and EQing is less successful for me. Also, if you get in a volume war on stage playing a P with flats, I think you will very quickly get the stink eye from your bandmates, and the sound guy may just throw his hands up and take you completely out if the FOH mix. In a disciplined stage environment, you are more likely to be successful, but in my experience, volume-disciplined stage mates with awareness of and respect for other instruments’ frequency needs are like unicorns.
So, for me, I love love LOVE a P with flats...it is THE sound of bass for me...but at nearly every single gig, I am reminded why I have to bring a bass with rounds. It isn't that a P with flats can’t work in my band, it is the simple fact that there are just too many things that have to be done (some by me to be sure, but mostly by others) to make it work acceptably live.
Sean Hurley and others of his ilk have the power to command a professional level of discipline that will allow them to do their thing with P and flats, and it sounds gorgeous.