Can you fix Magento admin slowness too?

Yes — admin tuning is part of every Full Optimization. Common culprits: (1) the indexer running on schedule but not actually completing between runs, (2) bloat in quote, quote_address, and sales_order_grid tables (we run cleanup with a safety-net backup), (3) the admin grid loading the entire product collection because of a missing index, (4) third-party admin extensions running expensive observers on every page load. After tuning, admin pages typically load in 1–2s instead of 8–15s, and the indexers actually keep up with catalogue changes.