Why are you singling out capital gains? Your argument works equally well for labor-based income, but capital gains are already taxed much less than labor.
I think the way to mitigate this problem is to index capital gains to the CPI and then tax gains like income. This cleans up the tax code quite a bit, stops favoring capital over labor, and balances out the pressure on the CPI with having a powerful group of people wanting to have it go up. At the moment CPI is probably under-reported and keeping social security and other inflation adjusted things lower than they would be otherwise.
The market can easily adjust prices for assets to factor in the cost of inflation and taxes.
But if you buy a stock for $1 and it goes to $2 as a result of inflation, you get taxed $0.5 on the $1 gain, but your resulting $1.5 has less purchasing power than the $1 you invested.
For practical reasons the state does not demand the tax until the accumulated gains have been realized by selling the asset. This makes sense for illiquid assets like stock in your private startup, but I don't think it should change the calculation of when the tax was incurred and how much. For liquid assets like shares in public companies, I think it would actually be perfectly reasonable to demand the tax on unrealized gains.