Do you really truly think that the rational thing for both parties to do, is steadily defect against each other for the next 100 rounds?

No. That seems obviously wrong, even if I can't figure out where the error lies.
We only get a reversion to the (D,D) case if we know with a high degree of confidence that the other party doesn't use naive Tit for Tat, and they know that we don't. That seems like an iffy assumption to me. If we knew the *exact* algorithm the other side uses, it would be trivial to find a winning strategy; so how do we know it isn't naive Tit for Tat? If there's a sufficiently high chance the other side is using naive Tit for Tat, it might well be optimal to repeat their choices until the second-to-last round.