As with most things, there is a real issue which was less of an issue in the past, and became more of an issue at certain points, but (a) it was never not an issue, (b) when it was less of an issue it was still a lot more of an issue than fans of that period give credit for, and (c) when it was more of an issue, it wasn't catastrophically bad the way some folks portray it to be.
Even in Ye Olden Dayse, being a 1st-level adventurer in a (say) 4th or 5th level party? Yeah, you're gonna be squishy as hell and there's a pretty high likelihood that things your friends wouldn't find too troubling could outright kill you. So that's a thing. Conversely, even being two full levels behind other characters in 3e, while not exactly a superhappyfuntime thing, isn't horrendously awful, "you're now totally useless" etc. It's definitely going to put you into an objectively worse position...but that was also true of 1e!
A level spread of 1-4-4-4-5-5 (unless the '1') is a hench) is going to be hell on the '1' in any edition. And it goes both ways: I've run parties in the past with spreads like 3-3-3-4-4-8 and the '8' just dominates.
Contrast how well each of 1e and 3e would (or try to) handle parties with characters of these levels:
1-2-3-3-4-5
3-3-4-4-5-5-6
4-5-5-5-5
6-7-8-8-9-11 (I just finished running this party for an adventure in our 1e-adjacent system)
For the first of those, 1e would do OK (I've run parties with spreads like this many a time) though the '1' would have to be careful, while 3e would either slaughter the 1 and 2 or completely fail to challenge the 4 and 5.
For the second, that's a breeze for 1e - many modules were written in the specific expectation of a spread like this, as proven by the pre-gen characters included. In 3e, our party had a similar spread for a while and the differences were very stark: the 3s often couldn't hit while the 6 hit seemingly every time.
The third is nothing to 1e but is huge to 3e - the 4 is an appendage, as I saw firsthand in play. (and this isn't personal griping, I was not playing the lower-level character in either case)
In the fourth, that '11' stands out like a sore thumb. In the adventure I just ran that character was a bit too dominant for my liking; though even one level lower would probably have been OK. In 3e, though the lower-levels would at least have more going for them, I suspect a single 11 would rule the roost power-wise.
My usual rough guideline for our system is that if everyone is within 2 of the party average and the mode and median are also close to that average it'll probably work just fine. We found that to very much not be the case when playing 3e, where even a 1-level variance was a big deal.
Personally, I think the bigger issue is that folks who played in early editions didn't really care that much, because...well, frankly, characters died left and right, so it was easy come, easy go. That's not really the paradigm anymore (for which I, at least, am supremely grateful). D&D characters today are not seen as something you casually toss into the woodchipper. Investment into a character is not the consequence of play, it is an expected input of play.
As a consequence, even though the difference between a 4th level character and a 6th level character is only somewhat more weighty in (say) 4e or 5e than it is in 1e or OD&D, you feel that difference more keenly because the game is designed with an expectation that you're invested.
It's not that the power gap between level N and level N+1 has grown that much. It has grown, but not that much.
From 3e to 5e I'd even say the power gap between levels has shrunk somewhat; 5e seems way better at handling mixed-level parties than 3e ever was, simply because of that flatter power curve.
The investment-in-character piece is a different discussion, one we've had before.
A further factor to remember about earlier editions was that the game was in some ways specifically designed to generate level variance over the long run, via:
--- staggered advancement tables (e.g. Thieves needed fewer xp to bump than did Fighters)
--- level-draining undead and other effects
--- level-granting or xp-granting items and other effects
It's that the game design paradigm is one that makes you notice the power difference more. It just plays better with groups that are more or less at the same level.
The game design paradigm also defines and uses level range differently.
When a 1e module says it's written for level range 2-4 it means characters within that range - no matter what specific spread - will find it a roughly-appropriate challenge. When a 4e module says it's written for level range 1-3 it means all the characters are supposed to be 1st level going in and all be 3rd level when they come out. That's a fairly major difference.