OK, so here's the other side of my story...
At the same time I removed my toe clips and went bare-bottom, I ADDED a sideview mirror that I found on the street. It's not a good one at all, but I think I like what it does.
Before this, when I went on long tours, I sometimes used a wide-angle mirror attached to my left glove (my own invention); however, I've never used a stationary mirror because the ones I remember from my childhood bounced around a lot and never really provided a useful view. I'm not sure what has changed, but this handlebar grip-mounted model has really impressed me -- enough so that I'm ready to buy one with a "real" mirror, rather than a plastic one.
The other thing I'm considering, though, is a helmet-mounted mirror, something I have never tried. Now, here's where the "pushing fifty" part comes in. My eyesight has gone from superhuman to "does anybody have a pair of reading glasses?" over the past decade. The full-sized sideview mirror provides a large enough view that I can, at least, see that SOMETHING is behind me. Would one of those tiny helmet mirrors be as frustrating to look at as my shrimpy new iPhone screen?