I don't think Universal v. Betamax applies. It specifically uses the word "time-shifting", meaning that it was meant simply to record a live program and watch it at a later time. Courts have subsequently rejected "phase-shifting" as an argument (see Napster). I do not believe Universal v. Betamax is sufficient precedent to the wholesale copying of your media for "personal use". I maintain that the specific facts we are discussing have never really been litigated and that the landscape has changed drastically since then, enough that courts would seriously reconsider Universal v. Betamax as precedent.
Down to the next point about obtaining a copy, I think there are two relevant points:
1. If you own it are you allowed to copy it?
To this I would personally argue yes. But I can see how copyright holders argue no. You purchase an item, not its contents. (When I think about the limits put on the aftermarket repair and upgrade market by hardware makers and the outrage that causes, I think there's a reverse logic that applies in this situation.)
2. Should you be able to obtain that ROM or copy because you purchased this item? (ethically, not legally)
This is thornier. Should I be able to download an ebook from a pirate site because I bought a copy of the physical book? What about an old nintendo game I bought many years ago? That to me is a more interesting ethical issue. I certainly did not buy a perpetual license for all forms of that work, but it's not like I can go pick up a copy of a game for my Android either. Of course, if I could pick up a commercial copy (Nintendo resells old games for its new platforms), would it still be OK?
But yes, I also have opinions about changing copyright law, or really reverting it to an older time. I do firmly believe copyright is a good tool to encourage the generation of art, knowledge and entertainment, but I believe that a perpetual monopoly on that content for a lifetime and for your children's lifetime (or companies) is counterproductive to that goal.