I know I do. I imagine this is more of a mobile thing because on steam you can probably be playing anything or looking at them websites.
But on the phone if I don’t have a match to play because it is not time yet or just want to stare at my collection looking at the levels and all the sweet covers you have collected since you started playing. It feels like I spend a minimum of 10 minutes a day somehow…
I do it both on mobile and on Steam.
Hell, I even look for X-Poles alliance when on Steam and look at my second account’ roster. And similarly, on mobile I tend to check out my main roster 
I also have this Excel spreadsheet where I type in all my progression. I can stare at it for minutes
Oh gosh I do this. I just look randomly at the art or at the levels they are all at. Whenever that ISO Spent spreadsheet comes around, I can do 95% of it from memory.
Some time when i get bored, i go and read all their biography.
All the time …
I tend to look through my roster casually every single day. Surprisingly, it seems to me I’ve been doing it more often on the computer, than on my mobile - I like the UI more, showing me much larger portions on one screen without scrolling. Also, every now and then I check out my teammates rosters, enjoying their growth. Creepy really, if you think about it 
I stare at mine then look at my alliance members and say to myself I need more ISO to level you guys lol.
I look at it so much i cant remember last time i looked at me in the mirror.. Ridiculous.. 
It’s sad and funny. When I am waiting I look at it..grumpy that I have no real reason to be on the app. When I do have something to do I look so I don’t have to actually play the matches…why do I play this game again? Lol
It feels comforting knowing I’m not the only one who does this. It feels strange when I remember what my roster looked like months ago in comparison to what it is now.
Sometimes on the iPhone I swear the covers are in 3d.
I do it a few times a week, under the guise of teaching my 3 year-old the names of all the characters. He knows all 40 (yup, even Director Unreleased) and regularly asks me, “Daddy, can we look at characters?”
Yes… yes we can. 
I look at them and try to figure out what character to level next and if that fits with my main team. I think I pray a lot for certain covers too while gazing at my MPQ “shrine”. “I hope I get another BP cover so I can push him over level 100” or “When will I get that last Psylocke cover I need?”.
All the time. Sometimes I let the game play for me while I just stare at the covers lovingly.
i call it “rosterbating” and i do it constantly. 
marc
I sit in my roster trying to convince myself not to spend HP on covers
“You are not going to do any better in events if you have a level 102 1/5/4 LazyThor instead of a level 92 1/4/4 LazyThor. You don’t even have the iso to level him. Just close the app. Close it.”
You need to quit staring at Moonstone.
I stare at it trying to come up with random goals. At first, they were goals like “get all my 1*'s off the first 2 pages of my roster”. Then it was “get everyone on my first page to 100+”. Now I start looking at the last 2 or 3 pages of my roster and trying to decide where to throw extra ISO so I can get the “never used” characters into an acceptable order. Like I dropped some ISO into X-Wolvie to get him to 46 just so he’d be ahead of Modern Hawkeye and Rags.
My current goal is to level my 5 cover C. Mags to 29 just so I can force Daredevil onto the last page of my roster.
I’d stare at it more if they actually had more stats in-game. Max stats, ability upgrade information, play time with each character, etc. All basic information that is already “in the game” that isn’t represented to the player in any manner.
lucky you, I get to learn names of some weird ponies…