Obviously I trust $BIGPLAYER’s setup. To name a few reasons: 1) their large user base makes it simply more probable that a given bug will be discovered by someone else than me; 2) they have a dedicated team with more experience and resources to spend on testing and fixing bugs; 3) their setup has been working for me for many years now.
These are simply symptoms of FUD. Using that line of argument, you'll always end up with the biggest players, even though there is no technical reason to do so.
> to implement some kind of monitoring that tests my self-hosted setup and alerts me by SMS
On the other hand, how would you check that $BIGPLAYER's mail setup works with any other email service? You can't. Could you blame anybody at $BIGPLAYER? In a free service: No.
So why would you want do put so much higher standard on your own setup than on $BIGPLAYER's setup? Just to be able to say: "Oh no, available technology is not good enough, I'm staying with $BIGPLAYER."
This doesn't make any sense to me.