I run several instances of exim, and they really aren’t all that difficult (but I have been doing it for decades).
As @coderanger says, the problem is not so much setting up exim (which is relatively easy), the problem is that verizon online, hotmail, live, etc, all automatically blacklist email sent from Digital Ocean (and presumably other providers) with no recourse, and no way to get off the blacklist.
How email providers can just choose not to allow legitimate email through and still claim to provide a service to their customers I’m not really sure, but that’s the situation. I was just about to look and mandrill (even set up an account), and also just about to move my main email server onto Digital Ocean with the intention of using mandrill for at least some delivery if not all), so this has definitely put a spanner in the works. Looking forward to trying looking at some of the alternatives.