Is it the main purpose of law to promote morality?

The law is supposed to codify a set of thoughtfully-considered agreements made on our collective behalf, which should help clarify where the lines are in lots of situations.

To have it infused with notions of right & wrong in the big sense, ethics, morality...at least in some areas...is not a surprise.

The law mostly exists to punish. What promotion that comes from it is not morality but enhancing the desire not to get caught and punished.

It stands to reason that if law promoted morality, prisons would be moral places.

it is to reflect morality and provide punishments for non-conformance.

The law was made by a bunch of people who were trying to figure out how everyone else needed to act in order for they the lawmakers to be able to do whatever the hell they wanted.

I don't think it's necessarily there to promote morality. I would say it is there to maintain order. Without some rules, enforced by some form of authority, things would descend into anarchy.

No, not at all. Morality isn't something to be legislated. The goal and focus of law should be strictly about keeping a functional and peaceful society. Not dictating morals. There may be some crossover where functional societal behaviours are also inline with a moral behaviour but not concretely. Morals are too subjective to be rationally and " morally " legislated and enforcing laws decided purely on a morality basis is tyrannical and unable to be enforced without yeah handed and dangerous authoritarianism.