SES uses account-level suppression lists, to avoid sending emails to addresses that has complaints, hard bounced or soft bounced a number of times. It does not automatically handle bounces sent over email, and I've not seen a provider out there doing that but I could be missing it.
We do manually monitor those however, by having the FROM address directed at an inbox that we monitor. Out of the 4M emails we send per month, we only get one bounce email back. And that's not really a bounce but a "please confirm you are real" bounce.
This could probably be automated with SES too, by parsing incoming emails and adding addresses to bounce list. For that 1 email per month we decided not to add that complexity.
Note: This setup is used for transactional emails, where users opt in via account creation and the first email sent is a verification email, to check that the address is real and that the user owns it.
However, my experience was that you also had to do something with soft bounces. For example, if someone's mailbox is perpetually full, re-sending to it over and over still can still eventually hurt your sending reputation.
If you keep attempting to email an address that bounces, over time, you may get marked as a spammy sender.
As far as I can tell, this setup doesn't do much with bounces other than quitting on a clear hard bounce from the end SMTP daemon.
This is one of the reasons email services aren't cheap.