I don’t think it’s as simple as this. This will end up catching normal people (any mortgage, automotive loan, etc) but may result in tricky accounting/loan structuring to avoid having literal collateral for the billionaires you’re trying to hit.
I don’t think that taxing unrealized gains is the solution either, but I also don’t think doing nothing is the solution. This is a very tricky problem without an obvious solution (and it doesn’t help that the ultra-wealthy can fairly easily influence lawmakers).
So just have it kick in above $5M/year or something like that, and have it only apply to securities as assets. Not a lot of ordinary people are taking $5M+/year in loans against their stocks.