One issue that comes up when you have one resource fueling different things, is that those different things have to be more & more carefully balanced against eachother, or the resource is just used to spam the best (broken) ones.
1e memorization, for instance, partially avoided that, since you couldn't swap spells around during the day, you still might memorize the 'best' spell of a given level more than once, but you couldn't just cast nothing else all day - 'mana point' variants, OTOH, let you do just that. Spamming was the 3.5 Sorcerer's strength, and, of course, in 5e, neo-Vancian casters get the best of both worlds. 4e AEDU didn't just put resources on different schedules, it made it very hard to set up swapping among them, so if say, a 3rd level encounter, say, was a little OP, it just crowded out the other 3rd level encounters, not everything else you might want to do with a 'slot' that day.
So as much as I like the concept of expanding healing surges or action points into some heroic surge able to heal or power dailies or whatever else, it'd run into that issue.