it does play out from time to time (see NFTs, 2008 housing market)
Brilliant classic example of exception proving the rule. Both NFTs and the 2008 crash were caused by a massive lack of fundamentals, not irrational shareholder panic based on a few unknown selloffs, so the fact that those are the examples you came up with of big crashes just shows how weak the original claim was.
Apart from anything else, it doesn't even stand on its own terms - if billionaires were required to pay wealth tax bills, then there wouldn't be any mystery as to why they were selling their shares.
No. Obviously they wouldn't wait en masse until tax time to sell on the same day. If you knew everyone was going to sell their stock at the same time, wouldn't you sell yours first before the prices started plummeting? And by the same token, if you knew there was going to be a load of selloffs at the end of the tax year, wouldn't you wait to do all your buying at that time?
There's just way too many pressures in both directions for what you claim to be a plausible scenario.