Edit: Sorry for the super long post, I'm just always looking for ways to make my champion more healthy to play as/against :)
Passive: Gift of the Drowned Ones
Pyke stores 100% of the damage he takes as grey health. Grey health will fall off after 10 seconds. Pyke can heal 15% of his grey health by gettting a takedown on a champion. This healing is increased to 30% of his grey health if he kills an enemy with his ultimate, Death from Below.
I'm assuming that you're removing his inability to build max health since it's not listed here? Also, are takedowns the only way he can regenerate his grey health or can he still pop out of vision to regenerate it?
If you're removing his ability to leave an enemy champion's vision to regenerate his grey health, you're going to kill the champion. Pyke's early game is already on the weaker side, making him more susceptible to poke is only going to kneecap him even harder. Removing his ability to regenerate on-demand also poses a massive problem late game as he'll lose 70%+ of his health in less than a second and won't be able to go in for a kill later to regenerate it. It's hard enough as-is to consistently land ultimates, tying his regeneration to that is just a recipe for disaster.
Pyke's entire kit is reliant on his passive, it acts as a leash and keeps him in line.
In my opinion, this is how Pyke's nerfs/"compensation" buffs should be handled. Each change is listed in the quoted boxes and my reasoning is listed in description below each ability.
Passive - Gift of the Drowned Ones
Removed: Pyke's grey health now slowly decays over time after having not been used for 5 (+1 per 15 lethality) seconds.
Personally I'd rather see changes to other areas of Pyke's kit (namely his Q + Ultimate) before we touch his passive.
If I had to make a change, I would give him a slightly smaller window to work with his passive or tie it to a support item. This means that solo Pyke would still be dead while also reinforcing Pyke's "high-risk, high-reward" playstyle. Forcing him to use his passive gives opponents more time to collapse on his lane partner and set them back, but making it scale with lethality and buffing other areas of his kit will make Pyke more of a threat in the mid-late game to make that tradeoff worth it.
Q - **Bone Skewer **
Reverted: Pyke's shortened Q now does 15% bonus damage.
Unchanged: Pyke's Q is still a single target ability and will prioritize low-health champions, high-health champions, monsters, and minions in that order.
Trade-off: Pyke's shortened Q will now only slow by 65% for 0.75 seconds rather than 90% for 1 second.
This was always a weird nerf to me. I understand that Riot wanted to hit solo-Pyke and reducing his tap-Q damage hurt his ability to slowly wear down his opponent and subsequently ult them, but it also felt really counter intuitive and went against the "either/or" nature of the ability.
IMO Pyke's shortened Q (I call it the "shotgun Q") should give more upfront damage as by using it, you're giving up your only ranged option. The tradeoff here is that it slows less and for a shorter amount of time, but the damage bonus acts as an incentive to use and increases it's reliability to knock someone down into ult range.
W - Ghostwater Dive
QOL & Fairness: While Ignited, Pyke's passive (Gift of the Drowned Ones) will not activate until the debuff is over. Pyke will still be camouflaged and only have his outline revealed.
As mentioned in the note, this is more of a QOL/fairness change.
I don't like getting ignited as Pyke and surviving because I pressed W, and I'm sure 99% of people hate wasting their ignite because Pyke left their vision. Leaving the outline reveal but taking away the passive regeneration until Ignite's debuff is over makes fighting Pyke less frustrating and rewards people who catch him in bad spots (as it should be.)
E - Phantom Undertow
Unchanged.
Honestly, I just really don't think there's a problem with this ability. Every assassin should have an engage/disengage and none of Pyke's major problems stem from his. If your champion gets bursted in a second or less, you need to give them a reliable escape to work with.
Maybe we could add back in the damage to monsters? Although personally I'm not a fan of that, I think Pyke belongs in the support role and should stay there 100%.
R - Death from Below
Reverted: Pyke's most recent assisting ally will receive 1 "Your Cut" piece. When Pyke would have executed an opponent with Death from Below, he will receive 1 "Your Cut" piece instead of the ally who got the kill.
Removed: Each execution grants one "Your Cut" piece to both the last assisting ally and Pyke. In addition, each enemy champion killed inside the X by an ally grants Pyke two "Your Cut" pieces.
I don't even really feel like I need to describe my reasoning for this change.
I hate this "Your Cut" change so much. Ever since it was released Pyke's banrate, winrate, and playrate have all skyrocketed. IMO Pyke's problems after the solo-gutting (because he was in a weaker state at that point) could have been remedied with other changes to his basic abilities, not by overtuning his ultimate. I feel Pyke gets rewarded way too heavily for landing his ultimate now and that the previous iteration was just fine.
Seriously, if one change is going to go through, it needs to be this one.