I think there is no need to be obsessive about either string brands, string types or on which bass to use what strings:
These days, you'll be hard-pressed to find a new set from any brand that doesn't well for what it is. They all differ in nuances of course. But I'm really a string whore and play anything that gets in my way, always interested to try out a new brand or type.
Flat or round, taped or half-round, coated or not? I like the variety of all. After having played flats for a couple of songs in a band setting, I enjoy the liveliness of rounds (as do most guitarists I've found out, it's what they are used too, outside of traditional jazz, guitarists never play anything but rounds). And I dig the "clear-pick-attack-followed-by-a-quick-decay-thud" of flats after having played rounds for a while. You can be to the point of obnoxious with flats too, think of Iron Maiden's Steve Harris. It's not necessarily all vintage sounds.
I've made - sometimes for the heck of it - the weirdest combinations of strings and basses with great results. I've put Marcus Miller signature strings on a sixties Bird even though I never ever slap - they sounded great, giving the bass Ric'ish zing while retaining gibson warmth and fullness. I've stuck tape wounds on my active EMG equipped Lee Sklar bass (probably the only one with tape wounds in the world I hazard to guess!) And the result is better than anything I had before, kind of acoustic with a piezo touch, but much more stable and full. Many of my fretless basses have tapewounds too. Two of my TBirds have flats - they still sound like TBirds don't worry. I even once had my sixties EB-2 strung with acoustic bronze wounds, that sounded great as well, the raging mudbucker compensating for whateer volume loss there was due to the non-magnetic bronze coating. I've put TI 5-string flats on my Ric 4003S/5 and it was the first time a set sounded nearly even on that bass beridden with string volume issues. I even had my Ric 4003S/8 strung with TI flat regular strings and D'Addario rounds for the octave strings and that sounded exceedingly well too.
So what I'm saying is: Outside of the obvious - don't play flats if you want an angry piano tone, don't play D'Addario Chromes if you like to bend, avoid TI flats if you like not only your G string tight between the cheeks - there are really no do's and don'ts.