The closest thing I know of are DigitalOcean "Droplets" that have software pre-installed.
Using their services I have made "Snapshots" of different "Droplets" I've installed software on that I use to start new projects now, including web, database, and email servers.
I decided to keep those layers separated to avoid potential conflicts with updates and upgrades and I can use the email server for all the web servers I spin up so that's a very fast and flexible approach for getting a SaaS up and running.
Running an email server on DigitalOcean's platform is probably not the best way to go for what you're talking about. Even they don't recommend it. Having everything ready to integrate with one or more 3rd party services is easy enough though.
That, by itself, would be a hard thing to market to developers right now, but I do think there is a market for it and that it's pretty big and mostly ignored.