The registration costs would need to be non-trivial to discourage abuse, which would harm legitimate small-scale innovators. Also, who decides (or validates) the "worth" of a patent? We would be replacing one regulatory nightmare with another.
You claim a value for your patent. It is treated as property and subject to tax if transferred from one entity to the next. The catch is that you can only sue for a certain percent of the claimed value. You can change the claimed value of your patent, but then you must pay a tax as if that was earned income. You would have to be allowed to set your initial claimed value of the patent at whatever you wish. Kinda the same way that when you start a corporation you can decide how many shares you have (like 1.000 or 10,000 or 1,000,000). But once that is set you can't just change them around without registering the change with the state.
In theory it would punish people who transfer patents a lot, but have almost no affect on people who register or hold onto patents. Since trolls thrive on shell companies, it would be very expensive to constantly transfer high-value patents.
If 50 states can figure out how to track every single car in existence I think the federal government can keep track of patents. Especially because you already budget tens of thousands of dollars and hiring a lawyer to get a patent registration as is.