As you've mentioned, regeneration is...
Reactive, requiring players to activate powers after taking damage. Using these powers proactively is possible but wastes a lot of their potential.
Clicky. You've got 4 powers on different cooldowns to manage if things go south.
Weak against specific debuffs like -Recharge, -Healing, and -Regeneration, it doesn't really protect itself like other sets do (Resistance naturally resists resistance debuffs, and most defense-based sets provide defense debuff resistance).
To that, I would also add these faults:
Almost binary in terms survival - the regeneration set is dominated by sustain-type powers. If you're feeling nerdy enough you can average out the health-over-time value for the click powers and end up with a rough total health-per-second figure. Any environment where incoming damage exceeds that value is not sustainable over time. On the other end of this, any environment where the incoming damage is below that threshold is going to feel easy, maybe even too easy.
Building upon that thought, regeneration is "shallow" in terms of damage mitigation. Compare it to other sets where healing is provided as a secondary concern to other forms of damage mitigation, and as a result the effective regained health is some multiple of the green number you see on the screen. An enemy can't directly remove the health regained though electric armor's Energize, for example, because that regained health is bolstered by resistances. They'd have to deal more damage than the heal provided to break even.
Regeneration is very old and has had some serious ups and downs over its lifetime. When considering changing a power set like regeneration, there are some constraints I try keep in mind:
Try not to require a respec: breaking this rule means players will feel like they need to respec or change their build in some way to get the most out of it, and that can be frustrating even if the end result is a universal improvement.
Introducing new enhancement types: adding a bunch of enhanceable defense to Dull Pain would prompt players to reconsider the balance of Heal, Recharge, and Defense enchancements for the power.
The cottage rule: the core purpose or intent of a power shouldn't be changed unless absolutely necessary. Swapping Moment of Glory out for something else entirely probably wouldn't fly.
Changes should make sense thematically. Changing Reconstruction to steal life from nearby enemies like dark armor doesn't make sense.
So to me this means we want to keep things thematically centered around healing, add more mitigation layering if possible, and attempt to make the set either more proactive or less reactive in some way.
Add debuff resistances to click powers. By putting them into powers that aren't active at all times, we get some variability in game play and perhaps allow for a player to make conscious tradeoffs. Even with something as wasteful as Reconstruction, there could still be some benefit in hitting it earlier in a fight.
Introduce the absorb mechanic. Absorb functionally works like a heal, but doesn't decrease downtime between fights since it doesn't contribute to the main health pool. As a bonus, absorb uses the same enhancement types that players are already using for this set.
Add a constant, low-strength absorb shield to Integration or Instant Healing, similar to powers you can pick from blaster secondary sets like Frigid Protection. This would let you shrug off some static amount of DPS without simply out-healing it. If we make the tick rate for this absorb shield frequent enough, it starts to look more like a "flat -X damage per attack" rather than a "+X heal over time". I think this makes a ton of sense for a power named "Instant Healing".
Add some amount of absorb to Dull Pain, either net-new or by replacing some portion of its current effects with Absorb. One option might be to consider the player's current health level to determine how much healing vs absorb it grants. At full health, you could give more +absorb and no +heal.
Crazy idea time: pick one click power. Make it activate automatically if the player's health drops below a certain threshold.