The huge upside to First Past the Post is that the electorate definitely understands why their candidate lost the election because it's so simple.
The purpose of Democratic elections is not something like "good government". We haven't the faintest idea how to do that. What elections do for us is enable bloodless transitions of power. The useless idiots currently in power can be voted out and you can replace them with the useless idiots you want to be in power instead if you can get enough votes. Will they be any better? Well of course you hope so, but the one thing I'm sure of it is that fighting a civil war over it would be worse.
So the problem to think about isn't "Which electoral system best satisfies Arrow's conflicting criteria in my opinion as an educated person who has spent a lot of time thinking about it?" but "What ensures the people who voted for Bob not Alice will accept that Alice won?".
If you're choosing a single person like the leader of your Executive or something equally consequential democratic elections are (along with sortition) one of the least terrible of the bad options you have, and complicated mechanisms like the Schulze method you're talking about are likely to mean losers are defiant so they're probably the wrong choice compared to First Past the Post or other simple methods.
If like Debian you're basically just picking the head of a club, it's scarcely matters how you do it, Schulze seems over-complicated to me but it's just not a big deal. Having democratic elections isn't important for this purpose anyway - nobody is going to kill and die for Debian leadership otherwise, but knock yourselves out.
