Don't forget how quick the pro racers are. Their exposure is far less, so they don't need to reapply sunscreen.
It's possible you burn very easily. It's also possible you're not using enough (it needs to go on quite thick), that you miss bits and burn in small areas, or that it gets rubbed away. I definitely overlap sunscreen with my jersey sleeves and shorts legs, but if I burn, it's at those edges. You can mitigate this: apply one dose of sunscreen first thing, before breakfast and before getting your rising gear on (or roll your shorts up and leave your jersey off). Be sure to cover further than you think you need around the edges, including gloves, where I just cover the backs of my hands, and around any wristwatch. When you're just about to depart, apply another lot of sunscreen. You probably won't get as much to soak in, and it won't double the protection, but it will fill in any missing bits. Letting the first dose soak in will protect against rubbing to some extent.
I did a TdF mountain stage (turned into a 200km loop, and with a modified start). It was won by Warren Barguil in 4:40. I was out for over 12 hours, or 11.5 hours discounting the descent the pros missed out on (they also missed out on a rather large pizza between the two massive climbs). That's a factor of around 2.5.
I started with factor 50 applied at about 0730, and topped up in the early afternoon when I was stopped in some shade anyway. That was fine, and I've got fairly pale skin to start with.
The pros do occasionally start with sleeves on. Thin ones ("arm coolers", though I suspect the name is more derived from "arm warmers" than accurate) are available that provide decent sun protection, though I haven't used them personally. With the right riding skills they can be taken off on a climb while riding with no hands; I've seen experienced riders do this. These sleeves are made from thin, close-fitting, and even fabric. They don't have holes that would allow spots to burn, but instead wick the sweat to the surface where it evaporates quickly, providing almost as much cooling as if it evaporated directly on the skin.
You're right that arm warmers get horribly sweaty. They're a useful stopgap when touring, as I found when I was surprised by how sunny it was in a notoriously rainy place, had no suncream with me, and got a little burnt.