Even if you don't spar, simply motivating yourself to go to practice can be tough. If you can walk into a room knowing you're going to be pinned and choked, you can walk into an interview/negotiation/meeting/date no problem.
When I did my first competition, locking eyes with my opponent knowing he will do everything he can do to choke me, break my joints and knowing I voluntarily put myself there, it changed me :)
I especially like how you frame your last sentence. Since martial arts can sometimes be uncomfortable physically, like you I have noticed is that things that used to be uncomfortable are not as uncomfortable as being pinned down by someone much larger than you. I consciously remind myself of this if I ever feel nervous about something, and it works almost every time.
I've also read the book by Goggins (loved it) and martial arts really build up your "cookie jar".
The entire experience, from the first days when I got triangled by girls half my size (choking my ego as much as choking my body), to competition days, with pressure passers and crazy leglock guys... It absolutely changed me - for the better.