Oversampling gives you headroom for aliases for the rest of the synth that is more vulnerable to it.
* Some people are still making this mistake, despite information on the (many) ways to do it the right way being widely and freely available!
There's some ways to do band-limited distortion but...they aren't nearly as widespread, easy, or universal as band-limited oscillators.
Ring modulation is funny though because you'd ideally want the sidebands to modulate down by default rather than filter them out, that's why you're using it.