The problem with bulk email is that the volume of spam has created a whitelisth/blacklist system. The primary value of third party services is that they are
not blacklisted and anyone rolling their own bulk email solution is likely to be quickly blacklisted because some recipients will move the newsletter to their junk folder on Gmail or mark it as junk in Outlook with telemetry turned on and those will be the primary results that go into the various spam filters.
From a different perspective, pretty much anyone who wants your newsletter probably already subscribes to other newsletters and their email is already in the third party bulk email service's database; the third party service is more likely to provide partial metrics on user behavior for users who don't want your newsletter; and most importantly if your SaaS is your business's primary product then building a bulk email service is a distraction and not something that creates much value for your users.
Good luck