As with so many things in AWS, it's left up to the customer to inform AWS that a) you're running a mail server, b) what the purpose/use case is and c) request they configure the reverse lookup associated with the elastic IP you've allocated.
Source: I've been running public facing SMTP servers in EC2 for years with no issues.
Still, unless you're running a server for a lot of people and you have tons of free time, you'll discover that it's more expensive than paying any of a bunch of people to take care of email for you.
You're absolutely correct. The cost of my AWS deployment in service of my personal email, and less than 5 other people comes in at ~$5.06/mo. The time, however, is the real cost. If/when I gain significant users, Fastmail would be at the top of my list of companies to consider.
As with so many things in AWS, it's left up to the customer to inform AWS that a) you're running a mail server, b) what the purpose/use case is and c) request they configure the reverse lookup associated with the elastic IP you've allocated.
Source: I've been running public facing SMTP servers in EC2 for years with no issues.