I think it'd work fine if there was a system in place to allow damage to be dealt out reliably and soaked without requiring bennies...
And really, dealing damage isn't THAT bad. The only reason it's bad is because the unlimited exploding dice mean that the odds over time inevitably tilt towards the enemies...which means that a battle of attrition is always a bad idea for PC's. We HAVE to deal damage QUICKLY and overwhelmingly, in order to survive encounters.
If that wasn't the case; if we could more easily deal with incoming damage, then dealing huge damage immediately wouldn't be as big a priority and the attack mechanics would become more manageable as well.
As it is though, any attack that breaches Toughness is incredibly threatening. The Shaken condition is quite bad, and only characters who have invested in Spirit can reliably get out of it. Moreover, attacks that breach Toughness usually do so because of an explosion, which means they quite often inflict Wounds as well...and therein we enter a death spiral where damage taken reduces one's ability both to fight and withstand more damage.
I mean, I make it sound unplayable and it's obviously not. It's not a terrible, horrible, game-wrecking problem. But over time this is the pattern I've seen in the Savage Worlds games I've played. The characters who get through battles reliably either focus on incredibly overinflated Toughness scores that even crazy explosion have trouble piercing...or they focus on hilariously overpowered attack abilities that focus on multiattacking (usually with automatic weapons) to force Shaken/Wound results in a single attack action.
That feels to me like it's driven by the inherent swinginess of infinite dice explosions, and how an expendable (and in short supply) resource is absolutely required to mitigate damage results.
I mean you say you like character-driven luck...but that's not what bennies are. In the system as-is you CANNOT spend bennies, EVER, on anything but soaking (or huge alphastrikes that MUST succeed) or you're HOSED if a fight breaks out. Maybe in a combat-light setting or situation you can use bennies for something other than desperately keeping yourself alive (and really, even spending one, you only have a CHANCE at avoiding damage; it's not a sure thing), but in something like Rifts? Uh uh. So it's not luck. It is, as you say, hit points.
It'd be like playing D&D if the GM sometimes said, "Hey, you can change this situation by spending 50 of your 150 hit points to do so."
Then the PC might say, "Well, the cleric can heal me..."
To which Savage Worlds says, "Hahahaha...no."
Who's seriously going to take that offer?
(^_^)