There should be a distinction between a false positive and an inadequate investigation, at least. I can agree to your proposition if the state is only liable for inadequate investigations.
If an investigation is carried out with complete objectivity (with they rarely if ever are) then I would agree that the state may not necessarily be liable for a false postitive, though some compensation to those wrongly convicted, comprable to what they could have likely made in the job force, should still be given for lost time as a matter of social justice. There are other, worse, ways in which we waste far more tax dollars.
I would even consider this (although I'm much more reluctant, in comparison to your first point), but eyewitness testimony should still be available as grounds for the procuring of search and discovery warrants, as well as for the questioning of other witnesses and suspects.
Oh, I certainly agree it should be admissible for gaining warrants, and I would say even admissible in a trial under certain conditions (more for describing conditions of a crime, especially in the sentencing phase, than identifying suspects), but as a general principle one should not be convicted on eyewitness testamony alone.