If you self host as an ALTERNATIVE to the 3rd party you have all of the same problems - more because you know about them, and the 3rd party can make all these claims you can't verify until they fall over with a "load balancer misconfig" story you also can't verify.
If you self-host redundantly to a 3rd party you have no special benefit (it does the same thing) AND the additional cost of a redundant infrastructure.
Why not just have redundant 3rd parties (so-called "multi-cloud") if you can't or won't trust your 3rd party.
It's like saying "I can reduce the risk of my rental car failure by owning my own car", assuming your own car you keep undriven in your garage, doesn't have a dead battery, no gas, flat tires, and proves to be unusable for hauling.
The "cloud" was touted as the fix for all that nuisance in self-hosting. Magically Jeff's bit barn would work to five 9s of uptime, and you could sit back and write your code, unshackled to infra. Until Jeff's bit barn went tits up.
I say the "cloud" is just another guys data center behind an API.
You wanna cloud experience? Put an API in front of your own servers and burn a $100 bill.
