I used the 4e example because I own and ran (converted) the adventure it comes from, namely Keep on the Shadowfell. For the 2-4 example I was thinking of L1 Secret of Bone Hill.
In KotS it's assumed a) that the PCs will all be 1st level at the start and b) that you'll bump them when the module tells you to, which it does at one point I remember clearly and maybe a second point that I don't remember as well.
You may or may not be surprised to learn that Keep on the Shadowfell is considered one of the worst adventures ever written for 4e--and, indeed, among the worst adventures ever written for D&D in general--by those who do actually play 4e.
Imagine someone coming to you and complaining about B/X, or whichever edition you like instead, by using as their example an adventure
frequently cited by fans of B/X(/whichever edition you like) as an absolutely awful adventure. Would you consider the conclusions drawn from that adventure unrepresentative?
You may or may not also be surprised to learn that both
Keep on the Shadowfell and
Pyramid of Shadows, which are both considered highly execrable by fans of 4e, were the primary contributions to early 4e by a certain Mr. Mearls. They're the only early-4e books that have his name on the front cover, IIRC. No few 4e fans blame Mearls for a small part of the hatred 4e got at its launch
specifically because the adventures bearing his name were SO bad.
This rather starkly brought home to me the power-curve steepness in 4e. Characters in my game don't bump nearly as fast and bump on their own schedules based on how many xp each one amasses. They were in the 1st-2nd range going in and still pretty much there when they finished; and while the rough degree of challenge at the start was OK, by the time they got near the end (where the module expects them to be 3rd level) the place was hell on wheels for them - they did really well to get through without a TPK.
I'm quite well aware that your preference is only a few levels per
year of weekly adventures. That gap will never be bridged; it's simply not how most people do play, and what minimal evidence we have suggests that most players find your preferred pace of growth glacially slow and thus lose interest in playing at such a pace.
And, again, you're talking about the absolute lowest levels of the game, which I specifically said
always have this kind of problem. Every edition--including whichever is your favorite--has issues with throwing 1st-level characters at higher-level stuff. Because 1st level is the lowest possible low, there isn't any lower you can go (though I personally would like there to be so, as I have said elsewhere). It's extremely likely that 1st-level characters in B/X are going to get utterly
shredded by an adventure intended for 3rd+ level characters.
What you say is true, however the level of an encounter vs the level of a party isn't what I'm looking at here. I'm talking about characters within the party being themselves of different levels e.g. a 4e party consisting of a Rogue-6, a Fighter-5, a Wizard-4, a Cleric-5, and a Warlord-3 (I'm going to do us all a favour and ignore multiclassing for these purposes). For 1e, that's a snap - change the Warlord to a Paladin because Warlords weren't a thing in 1e and that's a very typical group. For 3e it'd be a disaster and I'm not sure 4e would like it very much either. From all I can gather, 5e would do better with it vs WotC's previous two editions, but still not as seamlessly as the TSR editions.
My point generalizes to that too. If combats up to a common party level +4 are acceptable, then it shouldn't be a problem to go for a spread of roughly +5 above the lowest-level character or -5 below the highest-level one, where the PCs are within roughly 4 levels of each other (which you have quite handily done here) should do just fine. Average party level is 4.6, minimum 3. So fights up to level 7 should be perfectly doable, and the Warlord will level up faster because you need less XP to gain levels when you're low level yourself.
A fight of roughly level 4-5 would be perfectly fine for this group; anything from level 2 (an easy fight for this group) to level 7 (a tough fight, where the warlord will have to be careful) should work just fine. It's never been true that 4e characters could just
throw themselves at stuff--teamwork has always been essential--so yeah, in a level 7 fight the Warlord should probably be very cautious or rely on ranged attacks and the like, or focus on things that help their allies rather than things that directly push the fight forward. Likewise, with a level 2 fight, that Rogue is gonna be pumping out the damage, but that's fine--some fights should be easy and some should be rough, beyond just the chance that the dice go awry.