Read more carefully.
I read what you said. It is not correct
No one used the word spearhead except you
A mortar will also move with infatry.
Correct. This has nothing to do with the discussion
An assault gun does not have to be in shouting distance that is why radio are for.
Read more carefully. No one said it was required, I said it made easier. It makes it MUCH easier
The fact the assault guns where branch of artillery says it all.
It literally doesn't. What you mean to say is that SOME assault guns were a branch of artillery
Context matters