A budget is normally set and it is funded by property taxes as a ratio of the asset value compared to all other asset values in the county. If your home didn’t increase in value nor did anyone else’s you’d pay the same amount because that budget has to be realized one way or the other.
Some jurisdictions make this less transparent by taxing at a flat rate (x% of assessed home value) but that’s misleading because they determined that rate to set their budget to begin with. If there were a downturn in property values across the board that didn’t happen at the same time as a recession somehow such that the monetary outflow remained high (high employment for the local government, high costs, no deflation, etc) then there would be a budget crisis and they’d revisit that percentage.
The federal government sets a budget. Then taxes everyone's financial holdings in the same way as you describe (in the second paragraph) to meet that budget?
If I understand you correctly, the way it would work is that federal government sets a budget of $100. Alice has $1000 of stocks and Bob has $500 dollars of bonds. So Alice pays $66 of taxes and Bob $33. If next year Alice has $2000 dollars of stocks and Bob has $500 dollars of bonds. Then Alice pays $80 and Bob $20.
The proposal to tax unrealized capital gains would not tax them as ordinary income.
The proposal we are discussing does align capital gains on ordinary income:
“Long-term capital gains and qualified dividends of taxpayers with taxable income of more than $1 million would be taxed at ordinary rates, with 37 percent generally being the highest rate.”
Another proposal is to even bring rates higher than now:
“A separate proposal would first raise the top ordinary rate to 39.6 percent … An additional proposal would increase the net investment income tax rate by 1.2 percentage points above $400,000 … Together, the proposals would increase the top marginal rate on long-term capital gains and qualified dividends to 44.6 percent,”
"The proposal would impose a minimum tax of 25 percent on total income, generally inclusive of unrealized capital gains, for all taxpayers with wealth (that is, the difference obtained by subtracting liabilities from assets) greater than $100 million."