Couldn't they just send you a DMCA takedown request, then if you don't file a counter request and take it down, when it goes to court they can just nuke you for not following DMCA procedure?
Right. You counter their automated boilerplate DCMA notice with your won automated boilerplate DCMA. End result is the same - the have to take you to court.
IANAL, but the DMCA Safe Harbor is for hosting providers that want to keep their hands clean of their user's uploaded content. If you're hosting your own content, the whole procedure doesn't apply to you (though if your content really is infringing, keeping it up after receiving the takedown could be used as evidence of willful infringement).