These services are more trusted because they gained reputation. You gain reputation with time, especially when you are high volume sender. Additionally there are whitelists of “good” email services, so getting there will require a lot of time and work.
About SMTP servers, you are using system (BEAM) that was designed to write servers and SMTP is quite simple protocol. so why not use Erlang’s implementation of SMTP?
About external services, it all depends on the volume. SendGrid offers 40k emails per month in free plan, Mailgun is offering 10k, so if you are starting these numbers should be enough for start, and after that the proces are pretty low. So really rethink your approach to using external services.
