I don't think Stack Exchange would be keen to implement an extra protection mechanism to discourage dupes, but I suppose that would partly depend on how hard it is to implement in software. But if they did, where would you put the cutoff? I suppose 3k is a workable cutoff, since those members are expected to be responsible enough to cast close & open votes. OTOH, although many dupe answers do come from low rep users, there are some prolific dupe answerers with quite high scores...
On a related note, although dupe close votes cause an automatic comment, perhaps that comment needs to be more obtrusive. Or it could generate a special header saying something like "This question has n close votes pending. Please review the linked question(s) before posting an answer here. Also consider searching for alternative duplicate targets." You never know, it might help.
Incidentally, questions may be marked as protected by users with 15k+ rep, but that only prevents users with rep less than 10 from answering, and a question has to be at least 1 day old. So this mechanism is normally only used to protect HNQ or historical questions that have gathered a lot of attention. It wouldn't help much with the dupe situation, since the unwanted dupes are mostly posted when questions are fresh.
Stack Exchange have already given us an extra tool to deal with dupes: the dupe hammer. That is very useful on SO, it's less effective here on Physics, since there isn't a critical mass of hammer wielders. It's hard to get the required tag score, unless you're very prolific, and very good. On SO, it's not so hard to get a hammer by 10k to 20k rep, if you specialise in one language. Here, you may not get a hammer until 50k or so (just pulling numbers out of the air), and just getting points here is generally slower than on SO.
Unlike other closed questions, dupe questions aren't intrinsically bad. They can be useful signposts, and a little bit of duplication may be useful. But we have to close dupe questions to prevent the dupe answers from being scattered all over the place, partly because we want to make them easier to find, but mostly because we want to make them easy to compare, and for them to compete with each other for votes, rather than having numerous small voting pools with no simple way to rank answers from different pools.
A big part of the problem is that there's no tangible incentive to searching for dupe targets & casting dupe votes, apart from the warm fuzzy feeling of doing the right thing. This has been discussed ad nauseum on SO meta & SE meta. So I don't expect dupe-related points or badges to happen anytime soon. But we can live in hope. ;)
In the mean time, there isn't a lot that can be done. On some stacks, the chat rooms are used to coordinate dupe-voting, but chat here is rarely busy enough for that to be practical, and I don't think the chat room regulars would like the room to be swamped by administrivia.
I suppose polite comments on dupe answers are ok. On SO, I sometimes suggest that the author could have done a dupe search, or that they should have noticed that some dupe votes had already been cast. But some people don't take kindly to such comments, although you can probably get away with it if you outrank them in rep. :)