I don't think that claiming damages implies a worth that should necessarily be taxable. If I am in an automobile accident and my spine is destroyed, I don't think anybody would suggest that since my spine is worth something to me that I should have been paying taxes on it.
Paying taxes to ensure copyright protection would basically have the real world effect of pealing back default copyright. No works would be protected unless the creator went through the trouble of registering^Wpaying tax for that work.
I don't think society would be better off without default copyright, so copyrighted works must remain effectively untaxed "properties".
The problem I am having here is that you are conflating physical property with intellectual "property" just because you want to go after patent trolls. What you are proposing would not be limited in effect to the people you dislike though.
If Bob Handyman were to invent a new type of, say, catalytic converter, in his garage, this would be of immense value to the automotive industry. This would therefore be an incredibly "valuable" patent. (And Bob would of course have to patent his new invention, unless he were a fool.) ..But under your proposal he would then be responsible for a massive tax that he could never dream of paying. And if he didn't pay this tax, automotive companies would then be free to use his invention without giving him anything?
That is crazy.