Compacting mostly gets rid of reasoning tokens, and honestly it would be nice of reasoning tokens did not constantly follow every follow up query. Asking even a simple/trivial question can have Claude use thousands of tokens. Compacting is good for getting rid of those.
I've had Claude immediately fall back to its usual verbose style immediately after compaction.
To be fair, I've had it do that immediately after re-reading the output style instructions, too.
My chat history is filled with "Yes, I broke the language rule. Let me rephrase that and update my memory. — You already have that in memory — Yes, true, I ignored that" (because "Memory" is a yet another .md file)