You don’t need to “take it to court”; if the recipient of the DMCA complaint says to the host that they disagree with the DMCA takedown notice, the host is required by the DMCA to put the content back up (or, at least, return it to whatever state it would be in if the DMCA takedown notice didn’t happen), and it is then the responsibility of the complainant to take the other party to court.
Which the complainant will never do, in these cases where it’s obvious that it was just an overzealous algorithm flagging things it shouldn’t have—because actually pursuing damages for those situations are exactly the type of thing that make a judge issue contempt-of-court charges.