The exact rules could be tweaked to keep it from being a burden on families taking a second mortgage, e.g. if you borrow less than a certain amount in the tax year perhaps the rule doesn't apply. Use your imagination.
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.
People take out loans for much more or less than the value of the collateral. Do we ban that, or do we open up another tax/laundering loophole by letting the official value of a property diverge arbitrarily from a hypothetical sale value?