Everyone here talking about no email clients, IMAP and AWS restrictions is missing the point. Although you could use this as a personal account, or as a company. This fully automated system is a perfect ground layer to a number of applications with a very cleaver API.
Say you are a small startup, and you will need some email functionality? Give your web server access to writing to outbox and you can send email. Use the sender with + rules and you get replies with customerId, threadId etc. Need to show email interactions in your service UI? Subscribe to the notification channels. Need customer support platform, it is almost built-in.
If you don't see value in this solution, you probably never tried to setup infrastructure to receive email. In fact, at $work, I developed a very similar architecture and it is running flawlessly for 15 months or so. We just don't do all this git+lambda craziness, we just had already setup EC2 that we added some routes.