How old are you? Wearing braces makes your ankles weaker over time. Its just a stop gap. If you're an older guy just trying to stay on the court, but all means, strap up. But if you're younger and still have a decent amount of activity in front of you, I'd focus on strengthening exercises to try and fix the problem.
I had 2 REALLY bad left ankle sprains back in college. Did it once and could barely walk for 2 weeks (didn't help matters that I tried to tough it out with no treatment and had to walk a hilly campus). Went home for the summer and rolled it again even worse. (went in AND out coming down awkwardly on an outdoor court. I honestly thought it was broken) Then I had another one a couple of years later. Worst one I've ever had. 3/4 of my foot was black. It was then that I decided I was getting too old to deal with that crap, spent a few months in physical therapy and got it right again. I still roll it from time to time, but nowhere near as bad as I used to. Maybe its because its stronger. Maybe its because I'm older and not jumping as high as I used to. But knock on wood, I haven't turned it in a few years.
Some people just have genetically bad ankles. Others (like my dad) just sprain them so many times that there's no way back. But I'd exhaust all potential options before moving to a heavy brace.
Link? If true wouldn't taping do the same thing? Taping was mandatory when I played college ball.
Here's a link from a very quick google search.
3 of my best friends are licensed physical therapists. Obviously, my physical therapist is as well. They all say the same thing. Taping or a brace will help reduce the severity of an ankle injury, so when you're going all out in a game, it makes sense to tape or brace. However, your body has little muscles that are meant to provide support and stability. If you put a brace on them, those muscles don't get a chance to develop and get weaker over time.
College or pro teams don't want their guys getting hurt in the middle of a game. (which is why they might tell their players to tape or brace. I know certain D1 football teams require all their linemen to wear knee braces) But they do enough S&C work on non-game days (hopefully working these little stabilizing muscles) that it theoretically shouldn't hurt them long term.