(I didn't read the whole thread, but I'll toss here my 2cp)
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.
There was also a mirroring of typical gaming habits of that era. Video games for example were typically just like that: when you lost the game, you started over. In the past couple of decades, the paradigm changed to just keep playing, sometimes without even any sort of penalty.
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.
In combat yes, but you are forgetting all the rest of the game.
A first level PC in 5e can have a proficiency, a unique class feature, or spellcasting capabilities, that the rest of the party doesn't have. Someone non-proficient for example is going to have +0 even at 20th level, while the 1st level PC will have +2. The higher level PC might still have a higher ability score due to the boosts by level, but it may also not... Certainly the "everybody can try everything" mentality doesn't help in this case.
But in general it's only combat where there is a problem, and then it's the HP/damage difference which really matters. If you ask me, I was in favor of the early 5e playtesting idea for HP to start much higher (IIRC in the 1st playtest packet, everyone started with HP = Constitution score), but now it's too late for that.
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?
Because they are skilled in something the rest of the party isn't.
If you have no trapfinder, a 1st leve trapfinder with her +2 proficiency might be still better at trapfinding than a 20th level PC who is not proficient.
Again, unfortunately the "everybody can try!" concept gets in the way, at least with some skills, so for 1st and 20th level PCs to coexist smoothly probably the DM has to think of some added values to proficiencies (e.g. only allow untrained checks on routine tasks). But in general in 5e it's still much better than in 4e where everybody just got better at every skill by level.