What if they don't sell. What if you pay in shares based on price increase over the year and we then transfer those shares into a sovereign fund. Obviously that would be a progressive tax to mimic what is already done for income tax. That fund could then manage those assets and could potentially redistribute them in people's 401K (US)/RRSP (Canada) or make them grow to pay for pensions/fund projects (like Quebec CDPQ). In the first case (redistribution), people are unlikely to all sell at the same time (there could even set a hold period to be sure) and since the transactions would be small overtime it is unlikely to stir the market. For the second option, then the fund would manage it more like any large portfolio and it has an incentive to keep the stock high so it would not dump their new stocks (it would also benefit from stock buybacks).
The fundamental end goal of taxation is to reduce inequalities in a society to keep it functional and peaceful. As we are seeing unprecedented levels of inequalities that tells me that the system is broken. You can call it tax delay all you want, but if I can delay taxes for 50-60 years it has sufficient negative impact on society at the scale we are talking that it should be reformed.