That yom tov sheini is a punishment for not keeping yom tov rishon and not a lechatchila. And as the pnei Moshe explains, when you punish your kid for not cleaning up and they need to clean up double, they don't get credit for cleaning up double.
As I mentioned above, we don't really care about credit.
And even though it is מפני חטאינו גלינו מארצנו as we all say in מוסף, in a certain way it is קלקלתנו זוהי תקנתנו, where we merit to have another day of יו"ט. I see it
somewhat akin to what
Rashi says about שמיני עצרת.
But I guess in order to really appreciate it, you need to be connected to a Rebbe.
ETA: If one can call having another day of יו"ט a "punishment", I will take as much of that "punishment" as possible.