My discussion is to remove Galios DR from his current W and replace it with the On Damage Heal from his old W as well as provide context on why this change would make more sense in terms of lore. Furthermore, my goal is to provide a discussion as to why I think he should have his heal back and provide some of that same in-game feel and functionality of the old Galio with a more expressive way to play as a tank.
In Galios Biography in the League Universe Page he is referenced as the "Titan who 'ate magic'" and is even referenced in game that he 'eats magic'.
This can be interpreted as magic is a form of sustenance which can reflect itself in game with the on-damage heal mechanic.
In the lore we also know magic awakens him, but we don't necessarily see examples of it healing him. However, the first time Galio awakens (or 'comes alive') was after he was blasted by a strong source of magic which the "presence of a powerful magic stirred him to life".
Again there is an emphasis that his life is reliant to the magic that struck him as the claim 'somehow the accumulation of absorbed magic gave him life' was made. He hope's that one day there would be strong enough magic to keep him alive/active forever; this can also further that interpretation that his vitality or life is given by this magic.
Throughout his lore it is repeated that he absorbs or consumes this magic, and he does not mitigate magic in relation to himself.
Galio healing off magic damage in terms of gameplay fits well with his current theme and it was a strong part of his old kit/gameplay style: Bulwark being a fundamental part of his kit which was entirely lost in his new kit. Galios old kit had benefit on taking damage (W and R); Having healing and a damage amp respectively.
Galio does not have any of the on being-damaged benefit that his old kit had, or even any benefit of actually WANTING to be hit of any kind. Even with this on-damage benefit actually lending itself more to the current Galio lore than his older lore did.
Since it is not 100% accurate to what happens in lore, one may question why should Galio heal off of all damage rather than just magic damage then? My initial thought for that was; not every in-game mechanic is accurately or sensibly represented in the game (so this nuance can be forgiven). With abilities/gameplay such as Darius heal, Dravens infinite axes, Mundo's cleavers healing, Garen's 'magical sword' that falls from the sky, Fioras healing circle, Etc...
Galio in his current iteration does not really even really seems care for the DR however when deciding to use this ability, generally. Currently the way most Galio games seem to go, there are few times Galio uses W for the sake of its wind up benefit and ends up being a 'snap cast' taunt which provides him DR for a couple seconds after use.
Alternatively his heal would provide more situations in which Galio would want to use his W. Both of these scenarios have similar windows of power during their W usage, however the Heal gives Galio more opportunity to use this ability in game outside of snap taunt uses or before being hit by CC for maximum DR. He may use it in lane in a minion wave to heal up as stated previously, or focus on using W against enemies with DOT abilities, or even have more of a use as a Jungle Galio (if you're into that) for extra sustain. These are only some examples on how more thought can be put into usage of his W with a Heal that Galio with DR doesnt necessarily provide.
Overall between lore, more faithful mechanics from the older iteration, and more flexibility in use of the ability these are some of the reasons why I think Galio deserves his Heal back.