Ultimately, the reddit poster claimed three things as the reason for E6. In short - teleportation, raising the dead, and "quadratic wizard."
Quadratic wizard refers to the tendacy of 3e spellcasters to have several effects at each level - their lower level spells got stronger (ie, a a fifth level wizard would deal 5d6 damage with a fireball spell, while a tenth level wizard deals 10d6, both using a 3rd level slot), they gained more spell slots, they gained higher level spells that dealt more damage than lower level spells, even as they scaled. This is why it was quadratic - multiple things grew with each level, and that's before metamagic. Meanwhile, 5e wizards either a new spell level, or a different class ability. Its a linear growth. 5e casters are linear. (Technically, the Battlemaster is quadratic, since the martial dice grow in both sides on the die and in the number of dice you roll) Are casters still stronger than warriors? That's debatable; even if we say they are for the sake of argument, then we still can't say the reason is level 4 spells. Fireball is actually just as strong as level 5 damage spells. All spells, from level 3 through 5, are all roughly equal in power. There's no big jump in power until spell level 6.
This is keeping within the D&D tiers. 1-4 are "local heroes," 5-10 are "heroes of the realm," 11-16 are "masters of the realm" and 17+ are "masters of the world." All abilities within that tier are roughly considered equal.
The Reddit post then calls out teleport and resurrection magics as "beyond mortal ken." Ah, Dimension Door is a level 4 spell, and Raise Dead is level 5. Now we're getting somewhere. This explains why the post was complaining about level 4 magic. Now, I fully acknowledge that some GMs don't like teleports for how they can allow a party to get around challenges in dungeons. And some GMs prefer death to be final. And that's acceptable. But if these kinds of spells are an issue... can't we just ban teleports and raise dead magics? Are there really other spells out there that are so offensive starting at level 4?
If you want a E6 style game, lets address the issues at play. At what point are casters "stronger" than warriors? People often feel that magic trivializes non-magical challenges, so what magic is doing the trivializing? While we're at it, lets talk about feats too. Specifically, the Xbow Mastery, Sniper, Great Weapon Mastery and Polearm Mastery combos. These are generally considered to be pretty brutal after a point because of Bounded accuracy making that -5 penalty to be trivial. At what point is that going to be an issue? We should also keep that in mind.
E6, the original version, also served to keep attribute growth a bit more contained. To quote from the 3.x version - "Once transformed by their experiences, a character’s growth is no longer a continuous, linear progression. Instead, they specialize or broaden their abilities: There are still major differences between the master warriors and the veteran mercenaries, but it's not a change of scale."
This version is almost entirely comprised of ASI. Linear growth of abiltiies. They'll be pushing their attributes up to the next level, rather than broadening their abilities. That's kind of against the entire leveling idea of the original E6 rules. So, we should be considering other ways of growth rather than pure numbers.
Someone else brought up the issue that, without dead levels, there's a lot going on in classes we'd like to see. Such as, if I was playing a wizard, I would like to see getting my hands on the level 10 subclass ability. Or an eldritch knight being able to do the teleport when spending an action surge. Those are fun, often iconic abilities. A paladin might want to get their subclass' aura. A monk or sorcerer want to increase their class points, while a battlemaster would want more martial dice, even if they don't get more sides on the dice. How are we going to address this?