Having grown up in the 70s, when I got my first shi tty bass, first shi tty amp and first sh itty cab, I really think the "old school sound" was a rarity in the "old school".
Firstly there was a lot of distortion going on, and I hated distortion, my bass player mates hated it, everybody hated distortion on bass but it was almost unavoidable. If you wanted to be heard you had to crank it. If you cranked it, it distorted. End of.
Look at the live sound of even the most highly respected bassists from the old days -
Entwistle? Appalling. Distorted to hell, muddy and irritating.
Geezer? Sounds like he has two blown speakers going on there, overtones drown out the fundamentals, it's terrible.
JPJ? Even studio, what the hell was that on Heartbreaker? Distorted and played through a Leslie, you can't even tell if it's bass or guitar or what.
Cliff Burton? Don't get me started, was he using a Big Muff or what?
Not to say that a nice fat tube sound isn't great, it is. And there were a few old school tracks with a great bass sound. Verdine White with EWF had a great fat tone SOMETIMES but he still farted a bit and also plonked away middily sometimes which is also annoying.
A little overdriven is OK but most bass sounds in the old days were sh it. I remember reading an article with JPJ where he tried to develop a speaker that could handle good clean lows and still be super fat; he worked with Rickenbacker to develop a 30" speaker, which they thought would do the trick. Apparently when they plugged it in, it just did a huge farting noise and turned inside out. 8 x 10s seemed better!
And there are some new tunes that are good - I find that Bruno Mars respects the bass and often gets really close to that old school sound; I really enjoy the bass on his funky numbers.
So let's respect old school but don't get too mushy; remember those Acoustic amps and cabs like Jaco used to use? Never never quite good enough imho; Jaco's live sound could be appalling too.
And new stuff can also be good!