I think that there are more factors or questions that would need to be added in order for me to say agree/disagree. What units are we talking about with low deer numbers? I think many people will say that their favorite units are low in deer numbers.
Me personally, that is what I try and do anyway. In my first 6-8 years of hunting, we never really saw that many deer from the roads. Yes, I was a Utah road hunter but that is the way my family knew how to hunt. In the last 3-4 years, many things have changed. I've grown as a hunter and explored bow hunting and muzzy hunting. Now as a family, we shoot a couple elk every year so the meat isn't a big deal. We now try and pass up the little bucks in hopes for a chance at a bigger buck. This concept has been a huge adjustment, even for my dad. The first year I made him pass up 8 small bucks he about had a heart attack. He ended up taking a better buck later and then this year we passed up dozens of little bucks and he shot his biggest buck in my lifetime. This has been my evolution of deer hunting. I haven't killed a buck since '09 but I have chased more bigger bucks than I had ever seen the first 20 years of my life. Maybe I digress...
Anyway, I honestly don't know if an antler restriction would help. You have to think about how most of us on this site or any other hunting site are dedicated hunters in pursuit of that Monster Muley. You can't get the voices of the other 50,000 general deer hunters that don't get online. Many of them are perfectly happy shooting small bucks. They don't care. Sure they would like to shoot big bucks but on a family hunt or trying to put meat on the table, antlers don't mean crap.
The DWR, IMO, doesn't get how to manage deer anyway. The way that they turned those un-purchased archery and muzzy tags into rifle tags a week before season was a huge disappointment. Between that and the snow up north, many more bucks were killed than should have been. All these recommendations and ideas are great but if the DWR can't follow the plan anyway, then what good is it?
I guess I've talked a lot here. I don't think antler restrictions would do very much. I would support it but that is how I hunt anyway, like I said. I don't think it will ever happen though because of the uproar from the general public who want to put meat on their table.
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