It's not universal for them to show banding, it doesn't only show up at wide angles (unless you're talking about ultrawides and the sky, but that's because they're really a pair of polarizing filters stacked), and the 31mm isn't a wide angle anyway, unless it's being used on film.
Making your own might cause vignetting but probably not since it's a ff lens. Just get a cheap one and try it out, and if you don't like it, you're only out $15 or so.
I don't use mine very often. Mostly on really bright days, and especially if i'm using a wide aperture lens (one pretty much lived on my 55/1.2 til the filter glass came loose. I haven't replaced it yet, but now that it's warm enough that I'm taking photos outside more, I need to) and/or using fill flash.
I'm pretty sure I used one on most of the shots in
this album, because it was a ridiculously bright day and we were on a lake, so there was a lot of glare, too.