Why are they called "healing" surges?
Because they restore lost hit points.
"Damage": the removal of hit points.
"Healing": the restoration of hit points.
In your assessment, what is the difference between using a surge and regaining your surges?
Mechanically: to use/spend a surge is to draw on a finite resource to restore hit points. It requires either respite (second wind/short rest) or inspiration (a power).
In the fiction: spending a surge is pushing on through hurt/shock/dispiritedness, either because one has had some brief respite, or one has been inspired. In the technical language of this thread, it is mojo.
Mechanically: to regain one's surges is to replenish the above-mentioned finite resource. It requires rest (6 hours, no more than once per day).
In the fiction: having rested for 6 or more hours, one has either recovered from shock, dispiritedness and (relatively minor) hurt, or is able to push on again in spite of them.
So in the fiction there is not necessarily much difference between spending and regaining surges, but they occur at different places in the fiction - one after a brief respite or after being inspired, the other after a longer rest.
By the model you are describing there is no reason to have these two different resources because they represent the exact same thing. And you have just moved the flash healing to when the surges come back.
So you have changed a narrative disfunction into a needlessly convoluted narrative disfunction.
Losing hit points, and spending surges, may well represent the same thing in the fiction. They both represent having to push on, or try and endure, despite shock, dispiritedness, minor hurt, and comparable burdens on a PC's mojo.
Spending a surge, and regaining one's surges, may also represent the same thing in the fiction: having mustered or replenished one's mojo and pushing on.
But the context is different (both mechanical context and fictional context). Hit points are what the PC him-/herself brings to bear. Surge expenditure is what you can do with a brief respite, or with inspiration. (Note that a clerical Healing Word is, like a Bard's Majestic Word or a warlord's Inspiring Word, is on this model a source of inspiration. Divine inspiration - which has been mooted as an element of hit points at least since Gygax's DMG.) And surge recovery is what happens after a longer rest (typically, a sleep).
Whether it's convoluted I'll leave to others to judge. I don't find it needless, though. In play it produces dramatic pacing and reinforces strong (and fairly classic) tropes and themes. (The weakest mechanical component is the extended rest. It should be established on a narrative basis rather than an ingame time basis. The workaround I use is to link availability of extended rests to success or failures in skill challenges, which introduces at least a degree of narratively-determined pacing.)