When someone says "I don't like this proposal because I worry that important things will be underfunded", they do not mean "... because I worry that things will be funded less than people's willingness to pay indicates".

They mean, e.g.,

• ... because I worry that people may (quite reasonably) be ignorant of things that, if they knew all about them, they would want to be funded
• ... because I worry that such a scheme will give precedence to the interests of the rich (who pay more taxes and therefore have more power to affect what is done, overall, with tax revenues) but I don't actually care 100x more about someone who pays 100x more taxes and I don't think the government should either
• ... because I worry that even if each individual taxpayer has sensible and coherent preferences, aggregating those preferences by simple addition might send money to the wrong places
• ... because I worry that in order to make choices that actually serve their interests, individual taxpayers would have to put an inordinate amount of effort into learning and understanding the details of what the government does and what everything costs

Let's think a little more about the last of those. An obvious solution would be for there to be organizations that put in that effort so that individual taxpayers don't have to, and propose coherent allocations of tax revenues. Obviously any such organization's recommendations will be based (implicitly or explicitly) on potentially controversial opinions on facts or values, so we'd want there to be multiple organizations of this kind, each of which gives taxpayers some indication of what they care about and what they believe, and says what they think should be done with tax revenues.

You might notice that at this point we have approximately reinvented political parties. They would probably have some advantages and some disadvantages when compared with existing parties. It is certainly not obvious to me that they would be much better. The implied mechanism for combining "votes" is rather different (a sort of weighted averaging rather than picking a single favourite); again, it has advantages and disadvantages and might end up either better or worse.

What seems perfectly obvious to me is that you can't just say "importance is a function of opportunity cost, therefore whatever this system does is optimal by definition". Or, rather, you can and you did but you shouldn't. The kind of optimality guaranteed by Economics 101 is not the same thing as "getting what we actually prefer", and couldn't possibly be.

This is not a semantic objection. Your argument implicitly defines "important" as "that which will be funded by your system of government". This is structurally the same argument as the parable of hemlock.