R. A. Heinlein [IIRC] had a proposal to deal with this: the property would be taxed at the value assigned to it by the owner. OTOH, if the owner lowballed the value to avoid this, the obvious response to this gambit would be to force him to sell at that value.

Attorneys fees can be recoverable, but it is not the normal prevailing party analysis. The eminent domain provision in EAJA defines “prevailing party” as follows:
[A] “prevailing party”, in the case of eminent domain proceedings, means a party who obtains a final judgment (other than by settlement), exclusive of interest, the amount of which is at least as close to the highest valuation of the property involved that is attested to at trial on behalf of the property owner as it is to the highest valuation of the property involved that is attested to at trial on behalf of the Government[.]
28 U.S.C. § 2412(d)(2)(H).

The gov. can be millions too low, and still not owe you attorneys fees.

“Takings for anything should pay fair market value.”

The problem is defining fair market value.

Personally, I would define “fair market value” as whatever the current owner would be willing to voluntarily (genuinely voluntarily, which pretty much eliminates eminent domain) sell for.

If the seller isn’t willing to sell at any price (effectively setting the price at $infinity), or sets the price at 30 times what the government thinks the property is worth, tough, you go home empty handed.

“Just” is also a part of the equation. Where the taking is a home, “just” compensation may also entail additional payments due to the situation of the homeowner.

In NY, the problem of the “lowball offer” has generally been addressed by making the government (e.g., a town condemning a strip of land for highway use) responsible for both the ultimate value of the land as determined by the court after trial (minus advance payment) AND the land owner’s attorney’s fees. That is a big incentive for the government to make a fair offer.