The answer ought to be that it depends on the gig, who is paying you, and what they need. It should not be determined by technical limitations on the bassist's part. Best to be able to hang with any of the styles. Pizz, plectrum, and slap should all be part of a good working technique library.
That said, I personally have a hard time treating popular music like classical music and trying to get as close to the "original" as possible. To me, the player and the band in popular music really have an obligation to bring something a little bit fresh and new to cover interpretations. But, there are gigs where the guy who got the gig wants a particular thing played a certain way. I gut through a few of those every so often, but I'm not not long for the door when it happens. Not a good fit for me. OTOH, it is good to have the original recording under your fingers for reference.
I also find it is equally important to learn a bunch of the other parts in a given tune, especially the signature stuff. If nothing else, it helps build awareness and can further create spontaneous goodness, when tastefully applied.
Typical cover gigs do not require complete faith to the original recording, but you do need to understand key parts, play them well, and generally swing. That's the thing the crowd actually picks up on. Way more "does it feel good and sound good" than "is it faithful."
IME, YMMV.