Yes of course it is. Those places do more than just repair too, they also do a lot of work adjusting shoes for people who have, for example, one leg that's a bit longer than the other.
Now, you probably wouldn't repair an athletic shoe, because those are supposed to be replaced as they wear out, but anybody who has a nice pair of dress shoes or boots or loafers may want them resoled when they wear out because the rest of the shoe is still good, and it's wasteful to toss them. It's a fairly simple process that takes a skilled worker about a half hour or so.
The ones I have seen (Germany) usually are also key/lock smiths can replace your watch battery and maybe se other smaller similiar tasks or sell stuff like wallets.
Yeah, people have boots and stuff repaired all the time. Leather shoes in general can pretty much always be repaired, but others too. Now, you probably aren't going to repair tennis shoes or anything like that. They're made too cheap to be worth it.
Yes. A good quality pair of "goodyear welted" (the traditional construction style that allows the soles to be replaced) boots or shoes, well maintained and resoled as needed can actually be less expensive over the long term as well as more comfortable and stylish compared to midpriced fast-fashion disposable footwear.
They probably mean dress shoes which can be resoled, polished, resewn, etc. But yes modern shoes can be repaired, I have glued the soles back on a few pairs now that were otherwise in decent shape.