I agree with you on the by and large, but wouldn't describe belaying a lead climber as quite as demanding as you do (by all means, be vigilant at all times, someone's life is in your hands!). You can feed out rope from a grigri without putting a thumb in the mechanism, but it's a bit more of a hassle, and requires a bit more getting used to. I'm pretty much always belayed by my SO (who's a much better belayer than me, and doesn't disable the grigri when feeding) and get stressed out if someone else is belaying me and I notice that they're disabling the grigri while feeding rope.

It's definitely true that by far most injuries in climbing occur on the first 1-3 bolts, when it's still possible to hit the ground if you have too much slack or a bit run out bolts. Long run outs higher up can feel sketchy, but even a >5m fall high in the wall isn't really dangerous unless there are outcroppings or other stuff you can hit. Ankles might still take a beating though...