If you've resewn the button so much that the fabric is torn, it will have to be reinforced in order for the button to hold even with an anchor button. You can reinforce it with an iron-on patch on the underside. Iron-on patches can be cut to size.
I thought of something similar.
You could use any small piece of fabric, behind the inside of the jacket, and then sew the 2 buttons (one on each side, with the small piece of fabric sewed in also, between the jacket and the back button)
to strengthen the whole thing and the stitches.
I'd be careful of an iron-on , and would check the fabric first, because some have polyester components, that might melt.
Amusing to me, the posts about how much we love our old favorites, and want to keep them going, if at all possible.

Reminds me of an old favorite "childrens" story, wherein a coat, becomes too worn out, so is made into a jacket. The jacket gets too worn out, and is therefore made into a vest. The vest frays too much, and is modified and becomes a scarf....etc... till i think it's a bow-tie or something.

