I am not a bass player, but doesn't it all boil down to your style and the type of music you play?
In some cases, yes. At my age, Chris Squire comes to mind as the end-all and be-all of roundwound sound during the latter part of my "formative" years. He certainly wasn't going for old school thump on "Fragile" or "Close to the Edge", records that had quite an impact on the bassists I knew at the time.
These days, many bassists go for a post-modern zingy sound albeit with plenty of bottom, and, in some cases, severely scooped mids. I'm sure there are a lot of bands out there whose sound is, to some extent, dependent on that particular bass tone.
I personally feel that flats work for nearly everything I do. Classic rock, blues, standards and of course rockabilly/y'allternative. They were part of the sound I grew up with. McCartney is the obvious icon, but also all that hot Motown stuff from the early 60s, the Stax records, everything I heard coming out of New Orleans when I was a kid.
So I'm curious as to how many guys here have never even tried them. For you modern guys who never delve into blues and so on, there may not be any hope for you. And, frankly, flats may never do what you want them to do.
But I'm interested in the guys who play old-time rock and roll, I guess, or soul or R&B, but who have never had the opportunity or motivation to try 'em out.