Interesting thread. I agree with the many of the OP thoughts, though I too like the concentration mechanic. I think 5e spell design fell victim to its simplified design and many spells could have used a second pass and/or more play-testing. I'm not so sanguine about blanket removing concentration from a large number of spells, though I agree some could use it.
The devs seem to have made it so that most ongoing effects (other than purely utility spells) require Concentration with a few exceptions such as
Mage Armor,
Mirror Image and such. I would rather, in some cases, work with under-performing spells to improve them rather than blanket removing concentration in all but a few instances.
Damage spells that require an action to utilize on later turns.
Examples: Vampiric Touch, Witch Bolt, Flame Blade
Of these I think only
Flame Blade would be markedly improved by removing Concentration, the others have too many other problems.
Witch Bolt still has poor range and effect for a poor action economy, though it would finally allow a
True Strike plus
Witch Bolt combination that many initially voiced as the saving grace of the spell (The less said about how beneficial that combo actually is, the better).
Vampiric Touch does cantrip damage (to cast this, you have to be a 5th level caster, when your cantrips go up in damage) for a pitiful amount of healing, in melee...over multiple rounds. Not even many gish type builds would take advantage of this much, especially since EKs wouldn't see this spell (if they happen to spend one of their 'free school' picks on it to begin with) until very high levels.
I would rather keep the Concentration of
Witch Bolt and have it Grapple the target, with the target getting a chance to make a STR athletics or DEX acrobatics check to escape the grapple at the end of each round to get free and end the spell. Keeps in line with the flavor of the spell and gives it some teeth.
I would make
Vampiric Touch an instantaneous touch spell that does 7d6 (or so) necrotic damage to the target, giving half to the caster as healing. This is still risky, but can be worth the risk as it does much more damage to the target right away (thus increasing the likelihood of dropping it) and gives a more significant healing boost. Plus it could be cast through a familiar.
Defensive combat buff spells (that don't have any exploration utility)
Examples: Blur, Stoneskin, Protection from Energy
Not so sure about this one, as I don't want a return of "pre-flight" buffing check-lists and scry-and-fry of 3e, though I realize that is more difficult to do in 5e even without concentration. I get the impression that
Stoneskin is supposed to be used to buff an ally, though even then it is not exactly superlative. I would modify it to have its protection count against magical weapon attacks (like blade ward) as well as give advantage on Con saves. This might make it worth the Concentration and component cost, plus help with keeping concentration.
Protection from Energy could use an "At higher levels..." line that allowed for an additional target for each added slot level.
Protection From Evil and Good is probably a bit too narrow now that alignment does not play directly into it, I would change it to protect against all creature types that are not Humaniod or Beast.
Spells that buff or create weapons
Examples: Magic Weapon, Elemental Weapon, Shadow Blade
I'm less sure about these, though I realize that they are more likely to be used in melee.
Spells that augment weapon attacks (that don't have an ongoing effect)
Examples: Thunderous Smite, Hail of Thorns, Lightning Arrow
I could get behind this. I think most
Smite spells could have been reactions, to cast after you successfully strike an opponent and not needing concentration (though the ones with ongoing effects could still require concentration). This might make them too powerful/easy though. Spells like
Hunter's Mark, I would perhaps give Rangers an ability at level X to ignore concentration checks on the spell due to damage, similar to the ability Conjurers get with Conjurations. This prevents those who 'raid' the Ranger spell list from immediately getting the benefit as well.
Some additional spells I would consider outright dropping concentration on:
Flame Arrows - This spell really does not need it, and it seems kind of petty to add it, though it falls into the augment weapon attacks above, it deserves special mention.
Flesh to Stone - The target already has to fail an initial save to get a temporary intermediate debuff (thereby making creatures with legendary resistance likely to shrug the spell off entirely), then the fail 3 before making 3 mechanic before the final (though permanent) effect is applied. Concentration makes the spell too costly. Without Concentration, its not like the spell will be flung about willy-nilly until the very highest levels, as sixth level spell slots are too precious.