I think using stamina is an excellent way to do it. You can make a psionic armor that increases stamina regen rate, or a more powerful psi amp that can be used at long range and allow your soldier to avoid walking as much...or both.
Just guessing, but I think Nord already considered that option... since it is quite obvious.
(and we're talking about Energy here, not Stamina... Energy changes, Stamina is a constant)
(same as Morale changes, Bravery is a constant)
(same as -- maybe in the future -- Mana changes, Psi Skill/Strength are a constant)
However, Energy is already used for many other things... like walking, shooting, throwing, etc.
And it also regenerates every turn.
I believe Nord wanted a way to limit Psi spam by introducing a separate non-regenerating pool of mana.