I only recently started doing it (since coming here and learning about it). Like many others, I like the finished look of it and looking on the wear and tear of older quilts of mine where I didn't, I can see how it reinforces the area and keeps it from distorting over time.

A quilt judge (not police, but a real "judge"!) told me that most judges expect front and back of the miter to be sewn.

if you ever decide to enter a quilt into a show for judging or appraisal the judge will check to make sure your miters are stitched closed! it may not (matter) to you whether they are done or not...but judges do care ;-)

I didn't used to sew the miters down but after a quilt I entered in a show was criticized for the miters not being sewn down, I decided to put that little bit of extra effort into it. I was told later that that is a big thing with quilt show judges. Who knew? It didn't seem like a big thing to me.

I always sew mine closed, front and back.. I sew up one side, push the needle through to the other side and blind stitch back down, then continue sewing my binding down to the next miter.. I like the look and feel it is secure.. nothing can catch on it.. and nothing can get in there and hide (don't ask me what could do that, I haven't gone there).

I do not , nor do I intend to. I have never had a miter distort or open even after decades.

I don't sew down the mitered corners of my binding. But then, I use a very narrow binding on my quilts.
If I had a wider binding - say a 1/2" or bigger, then I'd probably sew them down so they don't gape.