I think it's weird that people cite Steve Harris as an example of what flats on a P sounds like. True, he did play flats on a P but he got a really cutting, super defined rock tone that is really unique and not the best example of the way that setup sounds for most people.
He also changes his strings before every show. Which means his flats never settle into that thumpy type of tone that flats are known for. IOW, if you leave your flats on for 1-2 weeks, that Steve Harris tone will be impossible to attain. You would be better served to get THAT tone from nickel rounds...you will get some of the warmth of the flats, but keep the "clank" for much longer than you would be able to with flats.
If you want to hear the absolute definition of flats on a P, listen to Jamerson. It's warm, vintage thump. It's undeniably cool but if you're in a hard rock setting and attempting to cut through the mix as the guitarists layer a giant wall of distorted guitar on you, you'll probably want something more zingy and modern, in which case you should go with rounds.
While this is also true, not all flats sound like the La Bella flats that Jamerson used. For example, D'addario Chromes have very present highs, even when broken in, and they work very well in a hard rock context. Though we should define "hard rock"...I'm talking about AC/DC, Jet, The Strokes, etc. If you are defining hard rock as Godsmack, AIC, etc., then I agree....there probably aren't any flats out there that would work in those bands.

