He actually can! ...In later books. In book 46, The Deception (Ax's perspective):
It was decided I would morph the pilot again. A physically fit adult
male was a convenient morph for our purposes. And my own technical
knowledge would also be useful. The others would ride in my pocket as
cockroaches. After I borrowed a uniform. The laundry room was
obviously the perfect place for that.
Dressed and with the others in my pocket, I carefully opened the door
and stepped back into the narrow corridor.
<Okay, Ax, you’ve got to find Chapman.>
<Yes, Prince Jake.>
Note that this conflicts with book 8, The Alien (also Ax's perspective):
Suddenly, I heard a thought-speak message.
It was Tobias, on patrol far overhead. Of course, no one could answer
him. Humans can use thought-speech only when they're in a morph. And
since I was in a human body, I too was restricted to spoken language.
Since the earlier books were written by K.A. Applegate herself, and the later ones were ghostwritten (and then edited by Applegate), it's up in the air as to which is more canon.