I guess I am going to be the minority opinion here...
I like flats. I've used them before, and love the sound of chromes on a P bass or a J bass, even the S.U.B. Mm copy I had for a while sounded great with flats
But I've never had any problems locking in with a drummer and providing the deep, tight low end that is so characteristic of flats with rounds. I love the fundamental, and having the bass just kick you in your chest, to make the groove the most important thing and not solo/wank off trying to showcase my abilities as a player, but I only have one bass right now, and it has rounds on it. I find it is alot more versitile than flats (there is a tone knob on my bass) and I can cover everything flats do to my sound and then also get the classic trebly, grindy harmonic roundwound tone.
I think I'm going to give TI flats a try sometime soon, but I'm perfectly happy with my Sunbeams.
Just my two cents
While I agree with you to some degree (as I've spent decades doing what you are doing), tone controls on your bass or your amp will not replicate what Flats do for the overall low end of your band's sound. I know, I've spent thirty years trying it.
I've explained my reasons in numerous other posts, but there is a reason we have a choice between flats and rounds...and many different kinds within each type.
I choose to support the band with a tighter, fuller sounding low end rhythm section by using flats. Everyone has their own reasons for what they're doing. It's all good. Different strokes and all that.