Companies have bureaucracies and bureaucracies are very much budget-constrained.

Companies can decide to do it however they want. They don't have to conform to a platonic ideal of a bureaucracy. A company expecting to grow its market share will give it's managers more leeway than one that's under financial difficulties.

What can happen, which is why you may have seen budget constraints prevent profit-maximising hiring, is that the finance dept is operating off older information than the managers in business units (or just is crosswise with them for any reason at all). You can definitely get a situation in which managers can't get approval to do profit maximising hires, but this isn't inevitable.

I can imagine that this is the dynamic which for actual x10 developers makes flexible YC-style startups more appealing than rigid FAANG-level companies.

Apart from the general difficulty of organising like this and actually evaluating the marginal revenue from an additional employee (it's hard enough to attribute to your existing employees!), this marginal revenue is likely to have diminishing returns as the company grows and from a risk management point of view you will want to have some margin so that you don't flip into losing money as soon as business slows a little.