I remember in old games, if your PC died you rolled a new one at 1st level and you joined back up with the party and continued on your way. Even if the party was 20th level, you still started at 1st. It wasn't that big a deal but it changed over time and now 20 years later it seems punitive, impractical and actually pretty weird.
First of all, there's the power disparity and the contribution the new pc can realistically make. I know we've all bought into bounded accuracy like it was a religious text, but a 1st level pc IS NOT "basically as effective" as, say a 5th level pc. The 1st level pc doesn't have the extra attack, spell slots, spell levels or hp that a 5th level pc has and will likely die in any encounter a 5th level party engages in. The only way this is workable is if the 1st level sits at the back and tries not to draw attention from monsters, which is not much fun for the player.
Secondly, there's the in-world practicality of picking up a lower level companion (that someone mentioned in the other thread): taking the extreme example, why would 20th level PCs pick up an unknown, unskilled 1st level pc? It just wouldn't happen unless they were the 'chosen one' POV character in movies.
Thirdly, DMs seem to justify it like this: "It's your fault you died so I'm starting you at a lower level to encourage you not to die!" This one I find the most weird and the most illogical but I know as a DM I've thought it at times. It's trying to turn something which is effectively a punishment into a reward when its clearly not.
So where does this come from and why on earth did it ever make sense? Is it a reaction to "everyone's a winner" sports activities? Is it some kind of weird DnD hazing?
Addressing your points in order:
1.) The power disparity for heterogenous levels in 5E isn't usually as bad as you portray it. You picked an extreme example (one 1st level guy in a 20th level party) but how likely is it that the very
first death in the party, ever, would happen at level 20? More likely you'd have one 20th level guy, some 14th-18th level guys, a 9th-level guy, and the 1st level guy. The 1st level guy will level up pretty quickly due to the shape of the XP table, and if you think 2nd level guys can't contribute in important ways I guess you've never run into a Diviner.
Even a simple Bless from a 1st-level cleric can be really nice.
2.) The experience I'm about to relate isn't as extreme as your 20th-level hypothetical, but here's an experience I had recently: mid-level party (5th, 5th, and 7th), after raiding a dungeon, received a diplomatic message from one of the dungeon's inhabitants with the request to deliver it to the king. 5th level guy accepts the letter and tells the party he's leaving to give it to the king, because that's what his character would do in that situation. Other party members are kind of taken aback, but okay, he's gone now and I guess we're down to two, and I as DM am like, "Okay, maybe I'll have you run the monsters this session then." But early on in that session, another plotline comes to fruition and one of the party's (unwilling) minions catches the "adventuring" bug and gets promoted to full NPC ("will gain a full share of the XP from here on out") and will become a 1st level character in a class of his choosing as soon as he gains 300 XP. Then to my surprise, the player of the missing 5th level PC volunteers to take over the NPC, Grindle, as one of his own characters. It makes perfect sense, so I agree. So now instead of playing a 5th level guy, he's playing a 1st level guy (now 2nd), in a party of generally much higher level--but it makes perfect sense from a roleplaying perspective, and the player doesn't view it as a punishment.
3.) I don't use as many exclamation points as your hypothetical DM, but I do let my players know that I expect all of their PCs to start from 1st level, and advance either with XP gained during play or else using the "character tree" rules. (I.e. when an in-play PC goes up a level, another character in the tree also goes up a level too, as long as he isn't higher level than the PC in play.) I don't claim that it's a punishment or a reward, but it is one of my rules. I
will admit that, as a player, I view advancing to a higher level as a reward, but it's only meaningful if it's earned--I dislike starting at high level; it feels like not having a history. (It's okay for a one-shot though because in a one-shot, nobody has a real history, just a backstory.) From this perspective, starting a 1st level character isn't a punishment, but it
is a necessary prerequisite to earning a reward.
4.) In 5E, it is really, really easy to avoid having to start over at 1st level anyway. I love to throw out Deadly fights, and so far my PCs have all survived every fight even when I thought they wouldn't (thanks partly to my use of the Morale rules in close battles) and rarely even get knocked unconscious. Even if someone does manage to die, in 5E you can be raised from the dead with a 3rd level spell (!!!), and you suffer zero long-term consequences. No Resurrection roll, no Con loss, no restrictions on elves, not even any serious time limits except on the 3rd level version (Revivify). Death in 5E is a resource drain (time and material component costs), not a career-ender. You practically have to go out of your way to die permanently.