Just to play devils advocate for a second, humans are inherently social creatures and even the greatest of introverts require social interaction with other humans in order to keep our sanity and mental health in check.
Additionally I think that where Linus and Robins family live is supposed to be a bit distanced from the town itself (you can see evidence of this in Demetrius’s rainy day dialogue) so his choice to live in the mountains still leaves him rather isolated.
However, Linus doesn’t appear to take care of his personal hygiene a lot asides from bathing in the mountain lake, if he was actually using the spa I would have some serious issues with it, but as it seems he just appears to stand inside the entrance of the bathhouse for the heat.
The real question is if he pays taxes! That bathhouse is presumably government funded!!