This is pretty much the situation that the tax is designed to combat - people using their assets to increase their wealth without paying taxes. So yes, if you did that, you would need to pay taxes on the new money in the refinance. I don't see an issue if that makes this business model unprofitable or untenable.
> If we do this to homes, and the wealthy move their money to a new place, such as venture capital, do we try and re-price those illiquid assets each year?
There's no need to price anything. You value the assets put up as collateral as the amount of the loan they are securing.
> If one IPO’s and they take a loan against the stock to buy a home, do you give them their previous year’s mark-to-market payment back to them if the stock goes down the following year and they get a margin call?
Nope. It's just like selling and immediately re-purchasing.
> Imagine trying to grow a startup and being worth X on paper with no actual gains or money in the bank.
Ok, but nothing happens unless you borrow against it. I'm not sure what scenario you are imagining here.