Seriously?
A character covering a wounded companion with a shield while they both move from one point of safety to another?
There are no existing rules for covering an ally with a shield as it is, so you would already be in improvisational territory to begin with.
Two characters joining hands to run through an area of fog or darkness and not lose each other en route?
Why would you do this
in combat? Outside of combat, there is no need, and in combat, I genuinely don't see the benefit.
Two (or more!) characters attempting to maintain a shield wall while charging or advancing - or retreating?
This would be a form of mass combat, no? Two people do not a shield wall make, and the phalanx-or-larger types of combat are simply not within the remit of standard D&D combat rules; it would be mind-numbingly tedious to play through every single soldier in a unit (most likely a century, hence
centurion) using the usual combat rules designed to give life to each individual character.
These aren't beneficial?
And that's just movement. Add in other aspects of combat and simultaniety allows two foes to take each other out, an age-old trope which currently cannot happen: IMO a glaring flaw. It also adds greatly to the fog-of-war side of things, where stuff is happening fast and not everybody can react in time.
You may as well just come out and say it: Initiative is and was always an artificial, unrealistic tool designed to make things
play smoothly even though it (by definition) prevents IRL physically-possible behaviors. Much like having a single value for AC for the entire body, or using a binary hit/miss structure for determining damage dealt. Your problem is not that the rule exists; it is that you know that the abstraction is (necessarily) incomplete. But, again, I don't see how these edge cases are actually that meaningful for most groups in most cases.
None of the above is
new. Unless I'm very much mistaken, this problem with initiative has been present for as long as there has been a game called D&D.
Indeed, the AD&D initiative rules (and possibly those if OD&D as well) were so baroque, specifically in an effort to make them comprehensive and having (as the kids say) "a rule for everything," that they actually were
pretty much playable even for the man who designed them. Initiative is, was, and always will be an abstraction with benefits (simplicity, ease of use, reliability) and detriments (failure to account for edge cases, woefully bad performance for large groups treated as individuals, vulnerability to being cheesed.) Games are a lossy compression method.
Edit: Further, I reject your previous assertion that more rules
without qualifications causes bad DMing. More
poorly-made rules, yes, absolutely. More
unexplained rules, certainly. More rules
made without utility, no question.
But rules which serve a clearly-defined and useful purpose, which are rigorously tested to ensure they perform their intended function, and which are clearly and concisely explained? I don't see how those could ever support bad DMing
other than intentional bad-faith actors. The "eliminate all rules and just play Let's Pretend" crowd has been up to this point
so insistent that we ignore or discount bad-faith DMs when it comes to abusing the absence of rules, something I and others have
consistently been willing to grant. Surely, what is good for the goose is good for the gander.