A button turns out to be below the fold on common small screen sizes that a new designer forgot to consider. A bad translation results in 90% of users in a particular country misunderstanding something. A JavaScript library doesn't work on a common Android phone you don't test with. Latency issues make something virtually unusable from the other side of the country because of a single badly written function that's easy to rewrite -- but you still have to catch it!
You need ALL forms of feedback. It's not a question of some being more important than others. They're all important and play their own unique roles. Analytics is for catching AND debugging all the things that go wrong at scale in the real world, as opposed to the artificial and limited environments used for user testing.
