As somebody who has been an early engineer at many startups, I would never use this in almost any case because a managed solution is just better. If I can pay somebody else to do something hard with zero maintenance so I can focus on shipping a good product, I’m going to do that every time.
It really depends on what you are doing. Even though I have a similar setup, we are still outsourcing customer support with a third party for now. But when you do need the data from emails, I would expect this solution to be a better choice.
Fiddling with outsourced APIs has a lock-in factor as well as not guaranteeing time-save if you don't have someone on the team already familiar with the third party product. I've certainly burned myself excessive outsourcing as well.
