Following this proof tree idea, this recent paper https://arxiv.org/abs/2102.03044 suggests to think of proofs of theorems as large trees, a tiny subset of which needs to be made explicit to convey the confidence the rest could be written out (if ever needed).
Verifying fully formalized proofs is cheap. What is expensive is to produce such formalized proofs. More precisely, to formalize a proof written in a typical math paper is extremely time-consuming and not so informative (that's why it's almost never done in practice).
