Automated test runs are for free

No. Automated tests will tell you what has failed but not why. The test team has to validate all failures after an automated run. There may be three reasons for a test to fail

  1. Regression
  2. Change in spec
  3. Bug in test code

Automation is cool

True. But it is costly. Some times bug fix takes 5 minutes and automating that test case takes 5 hours

When a feature is complete, there is no more work on that

May be true from dev perspective but not from QA. Test team keeps running the test code written for a feature. E.g. Windows test team runs tests written 15 years ago!!!