Why is there no 地 in 他读书很用功?
他读书很用功。


In this sentence, 用功 is actually used to describe 他, instead of the action 读书. The main sentence is 他很用功, where 读书 can be regarded as a subject clause, so you need an adjective. You can also say 他读书很用功的, but it is kinda informal.


  他很用功地读书。


As you said, 用功 is transformed from an adjective to an adverb, in this sentence, in order to modifier the verb.

I'm not familiar with how to analyze the grammar, if I'm wrong, feel free to point out.