I think the bigger problem is that you can up their bill by spamming them

It seems that you are expected to read email by viewing the contents of the S3 bucket. That's a pretty big caveat.

My take away is that you'd be able to receive your emails and customize the handling of every email.

i.e. emails are received and put into specific buckets/folders and then, per message, a process is triggered to do something unique (put into database, forward to another IMAP'ed box, etc.)