If you accidentally made a hamotze on a food item only requiring mezonot, do you say al hamichya or birkat hamazon for the beracha acharona?
I asked my rav (who is from Ner Yisrael in Baltimore) and he said that that the bracha on a item is conected to the food that is eaten only. The bracha acharonah is not (in that sense) connected to the bracha rishona. Thus if one makes the wrong bracha rishona, one should still make the correct bracha acharona.
He said that since the bracha rishona and the bracha acharona are separate bodies of halacha, the poskim do not discuss your case.
He also pointed out that the example given ("mezonos" bagels) is incorrect and you should have used cake. For example see What is mazonot? That is, your question is about making the wrong bracha rishona and you are giving a case in which the correct bracha rishona is indeed hamotzi, which would require birchas hamazon (according to many poskim). That example makes the premise of your question wrong. It would have been better to have given an example which is definitely (according to all poskim) mezonos.
He also pointed out that you could have used the example of water or fruit to show why the correct brachah acharona must be made even if the wrong bracha rishona was made and why it is not given as an explicit halacha.
There are discussions as to what must be done if the wrong bracha rishona is made (and how to fix it). However, especially with pas haba be'kisnin (mezonos), the matter is too complicated to put into a post like here and I would probably make mistakes in trying to write about it.