I avoided them for years as a younger player. I had a very strong left hand and figured I they were beside the point for me. I played mostly Telecaster back then. As to Bob saying that you can't bend down without a trem bridge using only left-hand finger vibrato, the young whippersnapper-me would have said, sure you can: bend up to a note above what you want to play, strike it, and drop the pre-bend. Also useful for the both sides of the note warble, you silently pre-bend up to the note and wiggle when you strike it.
Double stop or even some triple note chords I'd finger vibrato too. More complicated chords or open strings? I'd clench the guitar body and wring the neck. Looked brutal, but a Tele can take it.
So why am I going off topic a bit with this personal story: I now have electrics with vibrato bridges. I even have a Bigbsy equipped Tele. I float the trem on my main Strat. My old hand joints and weaker finger strength isn't up to doing what I did back then. They make some kind of vibrato things easier. For me it's kind of come down to my own variation on the old story told about B. B. King telling some other younger bluesman to go ahead and use light gauge strings because "Why do you want to work harder than have to?"
I never was a "Tele Master" with my young-man bends, though I liked making a racket. And I'm not Jeff Beck with a vibrato bridge now either.
They do take some extra setup to make them work as well as they can. They still can have some trouble even if you don't use them. Restringing a Bigsby is less fun (The Vibramate Spoiler is a great add on!). The alternate tuning issues? Well, it takes longer to re-tune as every string pitch change will likely effect other strings too, so you need to go back and forth on all strings a little more to make sure they are now all still right. Modern electric tuners make this less of a chore, particularly on a noisy stage. Some bridges (Strat style, when floating) are designed to have a balanced tension for string height. Changing to an alternate tuning can throw things off.
Yes, a string breaking in the middle of a tune means it may be best grab your back up guitar because you maybe seriously out of tune and it'll take a bit longer to restring on stage.
I still believe that beginners will be slightly better off to skip a vibrato equipped electric for their first guitar,
unless they specifically want to explore the things you can do with it or they wish to learn the repertoire of players who use them.