Do you any evidence this is is common? Plenty of heads of open source projects are hired by large companies. I've seen zero evidence of them not remaining independent but maybe I'm just unaware of those cases.
Gave you really seen that happen a lot? I can't think of many examples off the top of my head of open source project heads being hired by a company and given free reign to continue working exclusively on their project.
I don't know how you would see the evidence of the company imposing their will on the project - that's not likely to happen in public. It's also very likely to happen without any explicit influence taking place at all.
If a company hired me to work full-time on one of my projects, and I had to pick between two competing priorities for my time, I would naturally take my employer's own preferences and current challenges into account when making that decision. I wouldn't even consider that to be a bad thing.
It doesn't have to be full-time. The maintainer can be hired as a part-time contractor, or even consultant, and the contract can be specific to the project in question.
The problem with money translating to power is not unique to this arrangement, in any case. Donations can be similarly withdrawn, after all, so they also create an implicit bias. The only way to fix this is to make it so that people don't have to rely on such sources of income to sustain themselves.
