Whether it's better to use SendMail or an email delivery service will depend on your application. Right now the delivery service is likely the only solution if you need to send thousands of emails per month, anticipate even higher future volumes, and want to send from your own domain to many different destination email addresses. I heartily agree with your suggestion to enhance SendMail. Indeed there could be quite an opportunity for a strategic alliance between Wolfram Research and an email delivery service provider: Wolfram would gain highly specialized expertise in delivering email against the ever evolving background of spammers and countermeasures. The delivery service provider might gain a lot of new users from Mathematica and Wolfram Cloud applications.

Christopher, thanks for sharing. If I am not mistaken this adds html formatted mail.

If it is better, why wouldn't SendMail[] be modified to work like this?

Pieter van Bijnen points out the importance of sending email in HTML format and including inline images. Accordingly, I’ve updated the code in my original post to demonstrate such an email.

Also, don’t delay setting up your own email domain. The code in my original post sends an email from the Mailgun sandbox domain. But all your test, development, and production code should send email from your own domain. Domain setup consists of two simple steps. First, generate DNS zone file TXT, CNAME, and MX records: login to Mailgun (or whichever email delivery service you’ve chosen), follow the link to add a new domain, and enter a subdomain name. Second, enter these records into the DNS zone file for your domain: login to your domain hosting account and follow the appropriate links to add zone file records. Other than entering these records, subdomain setup does not involve any other actions on the domain hosting account. If you’re building applications that do both bulk marketing and transactional email, then keep their email reputations separate by setting up different email domains for each.