Well, in the case of losing actual emotions ... the thinkers would lose emotions too because as others have said, feeling in MBTI doesn't equal emotions. But if humanity lost the ability to feel emotions ...
We might all turn into ruthless psychopaths!
Or cybermen ...
And would no longer be able to: empathize, sympathize, love (except for the action-kind of love) be happy, peaceful, joyful, ecstatic ... goodbye music, stories, art, appreciation of beauty, charity, generosity, attempts of trying to help starving orphans, saving dolphins, etc., etc.
On the bright side, appeals-to-emotion logical fallacies would no longer be an issue!

Politics would be sooooo much tidier.
If the feeling functions were just lost from MBTI then you'd get all of the irrational feeler types (INFJ, ISFJ, ENFP, ESFP), going into dom-tert loops and then possibly falling into the grip of inferior functions and all of the rational feeler types (ENFJ, ESFJ, ISFP, INFP) falling into the grip of the irrational function. The thinkers would lose their lovely feeling functions which would be so sad because tert Fi ...

and tert Fe ...

