>Isn’t that generally a problem where people get slammed with huge tax bills on stock they aren’t able to sell and may not have the cash available to pay?

No, I can't say I've ever heard of that happening. You should be able to sell to cover. This will typically happen during an open trading window and brokerages will offer an option for "sell to cover".

>Why would we want to do more of that?

I didn't make a value statement one way or the other. I'm just saying your claim is wrong and maybe your misunderstanding of taxation on stock is not the reason that unrealized capital gains aren't taxed.