I have operated into and out of Sumburgh a fair amount and can certainly say I've never been desperate to get in
In all seriousness though, I'm intrigued by your point about people being overly keen to get into LSI (or any given destination with viable alternates) - in my opinion it's about getting
somewhere safely as opposed to getting to the destination at all costs. I can honestly say I've never felt pressure (as Captain or FO) to have to get in to a destination - if we see the lights at minima, great. If not, we might try again before heading off to the alternate.
You say there aren't many places to go from Sumburgh as if it's seriously isolated, then reel off quite a few. As well as the ones you listed, Kirkwall is only 80ish NM away with an ILS at both ends.