Bike-mounted mirrors often get in the way of grip location or controls, and are susceptible to damage from leaning the bike against a wall. More importantly, the mirror is often useless aside from one specific position/posture. This is particularly true with drop bar bikes - set up the mirror for rear view when riding on hoods, then when you're in the drops you lose the rear view.

Helmet-mounted mirrors work a little better than bike-mounted mirrors, because when you change position/posture you can usually tilt your head momentarily for a quick rear view. Additionally, a helmet mirror goes with you when you change bikes.

I've used the Cycleaware Reflex for years, it's a decent helmet mirror. If you leave the helmet in a hot car the 3M adhesive mounting pad will become unstuck, and the mirror falls off. A dab of Krazy glue will fix this. A hidden safety feature of this mirror is the mirror arm, which is steel wire covered by a thick layer of rubber. This rubber coating precludes the possibility of the wire arm causing a face or eye injury in the event of a bike crash. I starting using the Reflex mirror after someone posted a pic of their Take-a-look mirror dangling from their cheek, where the wire arm had been bent around and embedded into their face after a tumble on the bike.

Don't expect any mirror to give you a good rear view all the time - they are all a little fussy and work only OK in the best of times - but better than nothing, and safer than doing the "sorta looking backwards while moving forwards" thing.