Thurston, William P. "On proof and progress in mathematics." New Directions in the Philosophy of Mathematics (1998): 337-55. (arXiv abstract link).

I think that Thurston's famous essay supports the notion that simpler proofs are a mark of progress in mathematics, because simpler proofs lead to easier communication and deeper understanding, and

"The measure of our success [in mathematics] is whether what we do enables people to understand and think more clearly and effectively about mathematics."

An example is deBranges 1984 proof of the Bieberbach Conjecture, which was long and complicated but eventually simplified to a four-page proof by Weinstein in 1991 (and further "simplified" by use of Zeilberger's computer WZ method).

Answer from Joseph O'Rourke on Stack Exchange
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