Its primary uses are to send a message faster than speech would allow to an ally, and as a defense against wild (or sometimes infected) Rahi who don't really have morals -- if an evil being uses it, they could make the Rahi do something bad, but an evil user of a Mask of Strength could smash someone to death, etc. so the possibility of evil use alone does not make the mask considered immoral.
And if your question is whether Toa consider it immoral, obviously not. You could consider it immoral if you like but same goes for anything so I presume the question is about Toa tradition.
The Mask of Speed is what it implies -- speed, not strength. In some situations it could help you do something better than without it in the strength category, sure. Throwing a lightweight rock far will work better with speed than without it, and maybe (if it's light enough) better than strength. But if you want to lift a heavy rock for example, hitting it faster is just going to hurt you; for that you want strength. In general it seems to me the effectiveness of speed goes down with increased mass of whatever you're trying to move, and the desirability of strength goes up accordingly.
Punching someone with speed activated would not be like being hit by a car, because a car has mass and therefore stronger momentum (it won't slow down as easily). It would really be like being hit by a small rocket (that doesn't blow up). And I wouldn't recommend it -- you might snap your arm off, or lesser but also bad damage. If you wanna make it feel like a car hitting you would want strength.
In general, using speed as a replacement for strength is just not recommended period. Where it would help, the effect you're using would have to be small to be safe for you, so it's just a waste of energy. Usually it's better to flee, zoom around and attack from behind, etc. which is why you saw this sort of thing far more often in the story, if not exclusively.