I think e6 takes a sledgehammer to everything when it's only really the casters later that break things. Take the fighter, he has some more hp, makes some more attacks and possibly has a feat or 2 that enhance his damage. There's no need to cap his progression at level 6. It doesn't really do anything for the game. (Unless you just like the aesthetics of more heroic and less super heroic style encounters).
Caster progression due to higher level spells really do start harming the game.
A justifying observation is that in 5e casters and martials are fairly equal until level 4+ spells, but their imbalance is not the only issue for me with higher level play. My concerns are partly as you identify, but also form around game challenge, hit-point bloat and other matters. Here's the full text.
Some core elements associated with level advancement stop at 6th level. In summary, after 6th level:
- Hit points stop increasing with level
- Proficiency bonuses stop at +3 (but see below)
- No further cantrip damage increases or extra attacks are gained
- The highest spell level characters can ordinarily access is 3rd level (also see below)
- The optional Feats rules are used, but ability scores are capped at 18
- The optional multiclassing rules are not used
- Overall character advancement is capped at 12th level
These changes are further explained below.
Hit Dice and Hit Point Maximum
You gain hit dice and roll to increase your hit point maximum only up to 6th level. Your maximum number of hit dice is therefore six. Any bonuses to hit points count no more than six levels. For example, a 9th level character with a Constitution ability modifier of +2 gains 12 hit points, not 18.
If you choose to roll for your new hit point maximum, reroll any die that comes up 1.
Proficiency Bonus
Your highest proficiency bonus is +3. However, features that count proficiency bonus for uses between rests still use the standard value.
Cantrip Damage and Extra Attacks
Cantrip damage and extra attacks do not scale past 6th level. Thus, you gain no more than one extra cantrip damage die or weapon attack.
Spell Slots and "Enhanced Spell Slots"
Classes and sub-classes with the spellcasting feature gain "enhanced spell slots" in place of the higher-spell-level slots they would ordinarily access beyond 6th level. For full-casters that applies to 4th-level-spell-slots and higher, for half-casters 3rd-level-spell-slots and higher, and for third-casters 2nd-level-spell-slots and higher. Casters can only prepare or know spells up to the level of their highest ordinary spell-slot.
To cast one of their spells, a character can expend an enhanced slot of twice the spell's level or higher. Enhanced spell slots count at their full level for counterspell , dispel magic and similar - both for countering and dispelling, and being countered or dispelled - otherwise counting as half their level. That is also true for non-casting purposes, such as Combat Wild Shape, Divine Smite, Font of Magic and Arcane Recovery: count enhanced spell slots as spell slots of half their level.
For example, a wizard can expend a 4th level enhanced slot to cast melf's acid arrow - a 2nd level spell - counting it cast at 4th level for counterspell , dispel magic and similar, and otherwise as 2nd level. Another wizard could expend a 6th level enhanced slot to cast counterspell , automatically countering the acid arrow .
Enhanced spell slots are regained at the same time as other spell slots.
Enhanced Spell Slots for Warlocks
Warlock spell slots are capped at 3rd level, and then become enhanced spell slots that count as 4th (and later 5th) level for counterspell , dispel magic and similar - otherwise counting as 3rd level.
Ability Score Improvements
The optional feats rule is used (prerequisites are greatly loosened, and half-feats allow increase of any ability score.) Ability Score Improvements can't be used to increase scores above 18. Higher scores might be gained via deeds, sacrifices, perilous research, hard-won magic items, or as boons from supernatural entities.
Level Advancement is Capped
Characters cannot advance past 12th level. Beyond that, further features might be gained in the same way as miraculous ability scores.