Yes that's what algorithms like RePair and Sequitur do: they build the tree bottom-up by replacing frequent subtrees with a new rule at each iteration.
I think that this is also the basic idea behind the usage-based model in linguistics, a theory on how we learn languages:
The usage-based model is based on inductive learning,
meaning that linguistic knowledge is acquired in a
bottom-up manner through use. It allows for redundancy
and generalizations, because the language user generalizes
over recurring experiences of use.