That means on an average, you regain half your powers. Average being probably the better part of a campaign. Maybe two.
That does mean half the time you regain less than half your powers and half the time you regain more than half. Because everyone is rolling, that means generally half the party will get <50% and half the party will get <50%. So you'll have the awkward situation where half the party is relying on the other half, and will run out sooner prompting another rest. And potentially 10% of the time (which seems low but over the course of a level 1-20 campaign, is roughly a dozen times) the entire party will roll and get less than 40% of their powers back. And once in a campaign, everyone gets 20% back.
You bring up some points I would love to address.
1. I think you forgot about the full rest. There is a way to get back all resources, it's just not as easily accessible. But it should be accessible between most "adventures".
So the basic flow: At the start of an adventure the PC's will have all their abilities. They will face some challenges and use some of those abilities. I would say depending on the challenges different characters will use different amounts of resources here. Next comes the decision point. Of course the players will want the characters to get their abilities back. At this point they have 4 options, they can continue on. They can short rest. They can long rest. Or they can full rest. If they choose to rest at all they will need to decide which type of rest they want. A short rest provides a harder DC to recover abilities with a small setback. A long rest provides a moderate DC to recover abilities but with a moderate setback. A full rest will result in a major setback or failure of the campaign (but heck sometimes it is better to live to fight another day!).
In this example let's say a long rest is chosen. Keep in mind the following points.
a. Most characters still have some resources remaining
b. Not all characters spent the same amount of resources
c. The more abilities a character used the more they have a chance of recovering.
As such it's very likely that the characeters that used the most, gain the most back, but also still have the least remaining abilities going into the next leg of the journey.
2. Because of how things work above, I see your potential critique of some characters pulling more weight on a given day as non-problematic as what you are afraid will happen in my system already happens in our current recovery system. If anything my system will help alternate what characters do the heavy lifting from day to day as opposed to the same character doing the heavy lifting each day and then resting and repeating!
3. I think your 10% and 40% figures are off as we are talking about a 50% chance for each ability and not each character. Each character may have anywhere from 0-20 abilities they are looking to recharge. As such maybe 40 abilities that each have a 50% chance of occurring should have a much lower chance of occurring than you propose? Maybe you accounted for this but you can let us know for sure
