Not everyone wants to outsource transactional mail handling to a third party.
The major advantage to outsourcing it is that the people you're handing the job over to actually know what they're doing and are experts at it. Plus they can spend 24 hours a day checking this stuff instead of you.
The arguments for being in-house on absolutely anything but your core competency when you're an early-stage startup are really hard to justify.
Either way, my hat's off to them. It's a giant pain in the ass that can be resolved for less than $20 per month.
I would also suggest if you do go that route, have accurate metrics on everything. How much time are you spending maintaining what essentially is a separate product? How much is it taking from your MVP or is it part of it? If you can translate that to cost then you can judge how much offloading that service would be to someone that specializes in it.
Having worked on the IT and Biz side of tech companies (happily SaaS closing that gap daily) I can tell you the logic patterns are diametrically opposed.
IT = born problem solvers, nothing is too big, small or complicated BIZ = friction solvers, nothing can be too efficient
The struggle isn't that 'you' could do it (better, faster or even cheaper) in your mind... but that if isn't a core competency moving your business forward, write a check and let someone else handle the core. Break free from the burden of 'undifferentiated heavy lifting' and improve your core product.
We sell a SaaS solution and in turn I write ~20 checks to other SaaS providers a month to keep me focused on improving our customer's experience.