I didn't understand from your answer why validation and restriction of public access need to go hand-in-hand. When I left academia, I was no longer able to read tax-payer funded research papers without paying an exorbitant fee per paper. Are you saying that lowering the fees is would lead to "losing a ton of money"? Do you mean the publisher would become unprofitable, or become less profitable?
I am not aware of any alternative that can replace the current publication metrics for this purpose. The funding bodies have no motivation, capability or resources to make a replacement themselves, so that would have to come as a ready-made replacement in order to be accepted, and actually work (have usable content) for evaluating all current academic disciplines and academics out of the box (which seems rather unrealistic) so that a multi-disciplinary funding body can actually put that metric in their next funding round official evaluation criteria.
Hell, if you were guaranteed that your tenure committee actually read your full papers and then made their decision about the importance of your work entirely on their own, then you don't need any other validation of your work. But at that point we're sadly living in a fantasy world. In the real world academics making hiring decisions need external validation to judge their applicants. Figure out a better way to provide that without losing a ton of money and you're golden.