What portion of the 18 skills 6 saves + AC 30+ tools do you list for every character on your GM screen?

Oh please, you don't have to make this stupidly contrived. The base attributes, skills and AC are plenty enough. You might not even need the skills outside of outlandish expertise cases as even proficient skills are not that far off. You do realize the way skill scores are calculated is extremely predictable in 5e? Save DCs come from rules text most of the time, and besides, you probably should not be doing outlandish DC checks like 2 or 40 that often for it to become a trouble. When's the last time you've actually needed to know the players' tool proficiencies? You know the rogue can pick a lock and the bard can play a lute. If they have something more outlandish, they'll let you know.

Are you running games with 6+ players?

No, because my experience tells me too large groups lead to singular players having their time in the limelight so infrequently boredom is practically assured. Even then, a table with 6 or even 10 colums is barely wider than one with 3. Like literally, go boot up Excel, paste the skill names on the left column and you'll see very quickly that it'd all easily fit on one sheet of paper. The numbers don't take up much space horizontally.

Noticing that the Rogue has been doing very well on thieves tools checks and thus not making them roll to pick a lock is a clear example of the possible ways DM bias can occur, since another character (let’s say a Wizard with History expertise) with a skill bonus that’s just as high that hasn’t come up as much won’t get that same benefit.

This is silly. The solution to this is to take note of the wizard's specialties too, not to punish the rogue with having them roll pointless rolls. Your characters are not going to have that many outlandishly high scores that you couldn't just round up these outliers and make a note of them. From all of my experience with 5e and various DMs and DMing myself, most DMs make their players roll way too many damn pointless rolls. People forget the old rule of thumb that says that you should not roll unless both success and failure are possible and both provide a meaningful outcome that carries the story forwards. If the characters are not under time pressure and they can retry endlessly, just let them have it without a roll. The rolls will feel far more suspenseful when 90% of them aren't wasted on meaningless drudgery.

That all said, if you have auto crit fails on 1s, why are you not asking for rolls all the time, anyway?

You have it backwards. You should not be asking for rolls constantly because 1 always fails, you should only ever be rolling checks if 1 can fail! If 1 can't fail (or 20 succeed) you just don't roll. It's that simple. When's the last time you missed your mouth when trying to eat a sandwich? Doubt that's happened to you any time recently. Similarly, don't ask for rolls on trivial things. You don't roll to get out of bed, you don't roll to climb a set of stairs, you don't roll to not choke while drinking. Accept that the player characters are good at what they do. A pro does not fail a trivial task 5% of the time, so don't use a die to force them to. The rogue has picked locks his whole life and picking one is trivial for him, unless there is a specific circumstance that makes it otherwise, like time pressure, risk of getting caught or a particularly difficult lock.