You can have a tax system by applying it to earned, applying it to accumulated, or by doing a little bit of both.

Inherited wealth was already taxed at one point too. All money is taxed multiple times as it moves throughout the economy. That by itself isn't a good reason to dismiss any tax plan.

Theoretically there are good economic arguments to back up a 'wealth' tax as a replacement of income tax or an adjustment to it. In theory, it could discourage keeping enormous reserves and keep money flowing through the economy -- it'd essentially incentive corporations hiring and building out operations rather than sitting on a rainy day fund or paying dividends.

As I said though, in practice it just isn't entirely feasible even if you decided it was a policy worth pursuing.