A simple example: if you are poor and are on medicaid, it’s not possible to have a vasectomy without a 30 day mandatory waiting period to make sure that you are certain. If you are rich and have health insurance (or pay out of pocket) it’s completely fine to do it the same day.

That's still not 'wealth' but rather 'ability to pay the costs'. While correlated with wealth, that's not the same bar, and ability-to-pay is far more rationally related.

An entity paying – actually forgoing other possible expenditures of the same money, as in this example Medicaid or some other 3rd-party payor – should have some level-of-control. There's a budget constraint in effect - other priorities they are responsible for will suffer if this one is chosen.

But anybody, regardless of wealth, for whom it's important enough to scrape up the costs can skip that hurdle, in your example. There's no extra legal burden, of thousands of dollars of costs, added by the state just because they're poor. There's no extra complications the government forces onto the counterparty – the doctor – just because the patient is poor, thus deterring the otherwise-mutually-desired activity from happening at all.

(Of course, there are such complications if Medicaid actually pays – hence many doctors avoiding Medicaid-reimbursed patients/treatments.)

And in the end the poor patient still gets the treatment - unlike the permanent freeze-out of unaccredited investors – unless & until they bank $1,000,000.

Wealth filter on access to healthcare is an even bigger problem than wealth filter on investments.