Real estate can already be taxed via property taxes. Unrealized gains in securities can't be taxed the same way as their value is much more volatile, with potentially large daily swings. Texas makes up for the lack of income taxes with relatively high property taxes.
>In addition to real estate I might consider other property such as bank accounts, at least above a certain threshold.
Interest from savings accounts is already taxed. The wealthy don't hoard their wealth in bank accounts though.