There's a truism in the live sound industry: "You can spend £3000 on a wireless microphone system that will sound almost as good as a £10 cable".
And that's true. I'll use wired microphones in an place I can. However, there are a good many situations where cabled mics are simply not suitable, ranging from the stage musicals I work on to something as simple as a performer who is energetic and moves a lot.
I would never recommend cheap wireless systems. They are more trouble than they're worth.
However, once you get to a certainly quality level--and take some care with frequency selection, antenna spec and placement, etc. etc., radio microphones can work well and they are far from mediocre in sound quality. A KSM104 capsule on a good Senneheiser transmitter can sound far better than a crappy SM58 on a cable any day of the week. FM transmission is a mature technology and, done well with the right equipment, can sound just fine.
The last theatrical show I worked on had 22 head-mounted miniature mics plus a collection of handhelds. The all worked fine and the show sounded damn good.
This is a recording forum and we are likely not best placed to handle queries about radio mics for live use. I certainly wouldn't advocate trying to use wireless mics in a studio situation. But to say "affordable wireless systems suck because they sound like crap" is, to use your own words, crap advice. Sure, it depends what you mean by "affordable" but if you're talking something on the level of a Senneheiser
EW100 or 300 (or above) or the Shure or Trantec equivalents, their sound and reliability is FAR from crap.
Radio microphones have their place in the live sound industry and they are a proven technology that works well day in, day out all over the world. Practically every TV show or film you ever watch uses radio mics and they certainly do NOT sound like crap or even mediocre.