If a host does not follow the entire OCILLA playbook in every case, unconditionally, across the board, the host no longer qualifies for any safe harbor whatsoever. Then it's open season on copyright violations. Think $400,000 per song style open season.
The real liability threat remains third parties, not customers, and disregarding the prescribed counter procedure is handing them the keys to the bank. If you see a host playing fast and loose with the rules, for example your content not being restored in 10 to 14 days after counter notice with no further action, it's time to go after their registered agent.
The 512(c) safe harbor rules are clearly written in a transaction-specific manner rather than the way you describe, and every case I've seen on them has focussed on whether they were followed as relevant to the transaction and not addressed whether the host followed them "unconditionally, across the board". So, I think your conclusion is wrong.
Under what grounds? Taking down your content isn't violating your copyright. If they lose their safe harbor status, some future copyright holder could sue them, but I don't see how you could.
No, it doesn't.
The DMCA provides both a safe harbor for hosts against infringement liability (the take down notice procedure) and a safe harbor for hosts against any liability they might have for taking down content (the counter-notice procedure), but neither of these procedures are strictly mandatory, they just provide a liability shield for certain liabilities that the host may have had without them.
But most hosts have taken pains to assure that they have no liability in the latter case through terms of service, so there is little reason for them to be concerned with the counter-notice procedure.