I agree and disagree with this thread. You are correct in saying that Edo Tensei's don't have unlimited chakra. This is a misrepresentation of the tech. Instead the zombies likely have just rapid regeneration of chakra. Whenever they perform a tech, their chakra "bar" is likely refilled instantly. This however, does not mean it is infinite capacity wise. We've seen example like Mu with the Dust Release, and two of the Hokages not being able to make clones while holding the barrier. This is probably cause in life, Mu couldn't create a dust release attack with only 50% chakra either.
I'm hesitant to say clones should be used. Mostly because it makes zombies harder to seal if you have a clone that can interfere in the sealing process. I think a nerf that would be better than a chakra regeneration rate would be a limit to only one clone for the zombie, and the addition of either when the clone is out, the zombie can't use anything above B ranked techs (No Kirin, no rinny techs, no Sage Mode, etc) or if the clone is sealed, then the main is too. The latter would help with clone techs like the splitting tech, but would also apply to shadow clones.