1. IP address reputation - Keeping your IP addresses reputable is not a simple task. It requires balancing your emails for popular destination domains (gmail.com, aol.com, yahoo.com, etc.) across multiple external IP address. It requires you to deal with many different conflict resolution departments, who don't care about email, when a dispute comes up. It's practically a requirement to use a service like ReturnPath to maintain your reputation.
2. Throttling - When doing it yourself you need to throttle yourself. This is problematic on "big" days, especially when your marketing department wants to send many millions of emails for a big product push, promotion, or on days like black friday/cyber monday.
3. Hiring - A lot of people think sending email is easy. When you get up to the multiple million per day mark things start to fall apart. Do you have someone(s) on staff who really know sendmail/postfix/qmail inside and out?
4. Monitoring - sendmail/postfix/qmail are often times hard to monitor. You have to put together all of your stats. You have to put together all of your alerts. If you aren't really experienced with bulk email, you won't know what to look for and that can impact your reputation. Also consider your logging infrastructure. sendmail/postfix/qmail are noisy.
5. Cost - All of the points above play into the cost aspect of it. Is it cheaper to run it yourself, pay for all of the services and salaries, etc. Or is it actually cheaper to just use sendgrid/mailgun/etc. IP address reputation services are not cheap. Infrastructure cost is also something to consider. AWS IPs all have pretty terrible reputations so running this in AWS (and maybe other cloud providers) is a non-starter since no one will accept your email.
If you've got the expertise and you are sending a massive amount of emails then it might be worth it to run your own infrastructure, but at the end of the day, a single developer consuming an API is often easier and less problematic.