Mostly-irrelevant comment for many reasons, but I'll go there.
That's because in the studio, FX are typically added after the tracks are laid down. As for those vintage recordings by Jamerson et al: some of their tracks were overdriven (often via the recording equipment itself), and most were compressed. Paul McCartney's bass lines were heavily compressed, per a studio engineer who worked on 'em. These days, all bass tracks are compressed to some degree, as are other instruments and vocals. It's also common for reverb, chorus, delay, etc to be added; can happen even on bass. As I've said elsewhere: if you surf isolated bass lines on YouTube, you'll be surprised at how many are distorted or have other FX in addition to compression, even if they don't sound effected in the mix.
Of course that's the studio. The cool thing today is that pedal technology has improved to the point where it's nearly as good as studio technology. Of course that doesn't mean everyone should compress or distort or whatever outside of the studio. But the compression and distortion available today is at least as good or better than that used back on those 60s recordings.