.... For me, real life over the game - every time. A person dealing with an emergency shouldn't have to worry about how their absence affects the story of the game;...While the disappearance may hurt other PCs, foisting a PC on another player is much more likely to cause a player problem (arguments over what could have been done, arguments over items, etc.)...
We're really going to put the well-being of the pretend characters over this real-life human's emergency situation? The DM simply needs to adjust the encounter accordingly on the fly to compensate for 1 less PC in the action. It is really not hard... Worrying about immersion or verisimilitude or RAW or story at that point is not only unnecessary, it is heartless if a player is having a real-life emergency.
I've played this way for decades with a lot of different players. Nobody ever indicated they felt pressured not to deal with the real world. There is often a regret that they can't be part of the game, but this happens all the time. The game goes on without them, and they come back to whatever took place. Sometimes good things happen in their absence. Sometimes bad. There have been a few afk deaths. However, this is D&D. Only one of them was a death that stuck, IIRC, and that one was where the player tended to like to switch up PCs a lot.
I can't imagine someone concocting an emergency to avoid a consequence in game, at least not in my group. If it ever comes up then it would merit a discussion about priorities and bad faith gaming;
Invoking the Jerk Fallacy is not helpful. We're assuming good faith play. Good faith players want to play through challenges. Jerk players and jerk DMs can ruin anything.
Jerk players exist. Cheaters exist. Catching them, and dealing with them, is outside the scope of this discussion. However, my point is not outside the scope: A get out of jail free card for lying gives an incentive to do bad things that doesn't need to be there. Temptation is rarely a good thing if you don't want your apples bitten.
For the most part, none of the problems being presupposed here occur. And, again, this is with decades of D&D being played this way.
Nobody gets angry that someone else played their PC. In my groups, we've all had our PCs run by someone else at times. For the most part, when someone else runs the PC, they tend to be a slight bit more conservative with the PCs and there is rarely a problem for the PC (although being conservative does tend to create more risk for the other PCs).
There are times when PCs do just walk off screen in my games, as well, when the player can't be there. We do it when it makes sense for the story. Further, I've played with groups that don't care about the story at all and just have PCs disappear when the player can't be there, even mid combat.
However, that has caused as many problems as it has avoided (if not more).
In one game that is a stronger example, we were trying to solve a problem that required a MacGuffin. The player of the PC with the MacGuffin had a conflict, so his PC went off to do something (I don't recall what his character was doing). We thought it would not be a problem because we did not expect to deal with the MacGuffin during that session. However, that DM (who was really amazing) had some interconnection between the backstories of some of the PCs that we did not realize until we found ourselves deep in a 'dungeon' and realized we needed to use the MacGuffin, but that there was no realistic way for us to get the PC with the MacGuffin back to us in time. The DM had a choice to break the story to force the PC back into the story, to stop the game earlier in the night and tell us we had to have the other PC (which would have been a huge spoiler and ruined a lot of his hard work), or let us walk into a dungeon knowing we were going to fail a major challenge in the game with no chance of success. If the PC had just been with us, it would have changed the course of that campaign. There was a little frustration that we failed (which had major impacts on two PCs) because the player missed the session.
Further, when a PC is not there, it often changes what the players decide they want to do, which has often put the DM into improvisation mode as the PCs wander off to do something other than the thing the DM had prepared to run because a key player for that activity is not there. I'm fine improvising, but the best sessions I run are when I am prepared (especially during the current online era).
I play in, and run, story driven games. Writing out PCs causes a lot of problems when you have story driven games with interconnection. As it hasn't caused any real problems in 35 to 40 years of gaming, I'm not likely to change how I run games.