Isn't that the point though? The host receives a DMCA request and take down the content, they are perfectly safe (safe harbor provision etc)

You (the author) come along and say, no it isn't illegal - please put it back up. If they put it back up don't they lose the DMCA safe protection? They are publicly siding with your claim that it's legal.

Also there is the practical point that a takedown notice simply means clicking a link on the host's site or emailing an address. Getting it back involves sworn affidavits, visits to lawyers an trying to find a human contact at the hosting company.