None of the available Stamina heals are viable under heavy fire, Stamina healers are impossible.

Eocosa

As some people already stated, I believe this is intentional as a different form of mitigation.

Stam users can block longer, roll more, bash (admittedly some magic abilities also interrupt), more passive mitigation through medium armies higher rating (a wash when comparing heavy armored tanks), and have some minor HoT such as vigor and bloodthirst. Admittedly with DB they did just receive a better shield as well with the change to bone shield.

Magic users get access to shields and much better heals through restoration staff. They simply can not dodge or block as much and have a lower passive mitigation through armor rating.

If stamina users received a stamina heal weapon (idk some kind of bard perhaps?) to maintain balance they'd either have to lose their improved blocking/rolling capability which goes against stamina being almost like "fitness", have medium armor lowered to light armor ratings, or something entirely more radical such as lower damage potential to keep a risk vs reward element opposed to every simply going stamina.

Different damage styles and different mitigation styles can apply to magic or stamina (magically blocking with shields or physically dodging the attacks), but it seems kind of difficult to truly justify a stamina heather then simply because one feels it should be there.

My two septims anyways!

Amdar_Godkiller

They reneged on the Stam Shield. That's not happening. And I'm cool with that. Stam doesn't need shields. 
We dodge as a defensive maneuver; But we need heals because dodging isn't as OP or full-proof as hiding 
in a magic bubble; and it deserves at least as many as magic has, if not way more.

I think Stam heals should function differently. I think they shouldn't be bursty, but rather gradual (but 
consistent and long) HOTs that can be layered for greater effect. 

Think of it as an Army field medic build.