Hit Dice are like every other rule in the game... they will be exactly what one DM and table needs to make the game sing for them, and a completely superfluous appendix-like appendage that might as well not exist for another. So you can't make a "One size fits all" set of rules around Hit Dice that will work for everyone even if you wanted to.
After all... it's not like Healing Surges were 100% effective across the board either. Many folks talk about them being the most useful method of "attrition" they've seen in D&D... but I know at my table for the 6 years we played 4E (between its debut and the debut of 5E)... I think I only saw someone run out of Healing Surges once. That's it. Not a single other character in any of the campaigns I ran ever came close, so the use of Healing Surges did not represent "attrition" at all. They were just additional HP to gain just like 5E healing spells are just additional HP to gain. And that's entirely due to how I ran and run my table. It's entirely on me. So I do not in any way discount their use as an attrition model for 4E players... I just know they weren't that for me. And thus Healing Surges mirror Hit Dice the same way-- exactly the rule one table uses for the effect they want... a shrug of the shoulders for another.
After all... it's not like Healing Surges were 100% effective across the board either. Many folks talk about them being the most useful method of "attrition" they've seen in D&D... but I know at my table for the 6 years we played 4E (between its debut and the debut of 5E)... I think I only saw someone run out of Healing Surges once. That's it. Not a single other character in any of the campaigns I ran ever came close, so the use of Healing Surges did not represent "attrition" at all. They were just additional HP to gain just like 5E healing spells are just additional HP to gain. And that's entirely due to how I ran and run my table. It's entirely on me. So I do not in any way discount their use as an attrition model for 4E players... I just know they weren't that for me. And thus Healing Surges mirror Hit Dice the same way-- exactly the rule one table uses for the effect they want... a shrug of the shoulders for another.