Using HD for more things in 5e

[Arkhios]

0.5*2=1
You roll a normal hit-die, with constitution modifier, to recover hit-points as normal. It just only COSTS you half a hit-die from your pool.


You keep it for the same use later, unless your pool recovers to full, at which point it becomes irrelevant.

That clear enough, or should I provide an example?

I admit I made that question sarcastically, because while I see what you intended, I don't think this is a very good idea.

Why? Because, if you only ever used a one half a hit-die for this, and were to use your Hit Dice later to regain hit points during short rest, it leaves a lot of wiggle room whether the one remaining half a hit-die can or can't be used in that purpose.
Personally, I would be inclined to say no, because using hit dice to regain hit points mentions nothing about using halves. In other words, your mechanism renders the other half useless for anything else, and in so doing, makes resource tracking complicated, even if only a little.

But, that's just me. YMMV, of course.