I think the reason for it should be from the scope of negation.
Let's read this conversation:
A: I don't want to eat the pizza.
B: Me too.
To me, it does not make sense, because without a comma between me and too, the opinion of response of B can be read ridiculously as "Not that I want to eat the pizza more", which is definitely different from the meaning B wants to convey of "I don't want to eat the pizza either", so that native speakers seem not to prefer to place 'too' at the end of the negative agreement to avoid misunderstanding.
Based on my thinking, I think these following options could be acceptable as a negative response in the conversation:
The first option adds a comma. B: me, too (but I think that in speech it is barely used by the reason)
The second option locates 'too' before the scope of negation. B: I too don't want to eat the pizza.
Is my thinking correct?