I know this is an old discussion now but I stumbled across this and wanted to add a conclusion I think I’ve reached about the difference in was/were VS “would be” in these sentences, after a decent amount of analysis...
This may absolutely differ across dialects, but for mine, I sense that we can wish for actions to happen, and we can wish for states/conditions/descriptions/facts to be different (I will call these “states” but in a very broad sense).
I would use “I wish X would....” if I’m wishing for an action... but I would use “I wish X was/were...” if I’m wishing the state of something were different from what it is... so, for example:
It’s raining (a state) and I wish it were not raining (an alternate state)... here, the only truly natural way for me to say this is “I wish it weren’t raining” (and I recognize that many people would use “was” rather than “were” here).
Now if I turn that into an action... rather than referring to a state of not raining, if I say I would like the action of “stop raining” to occur, I’d then say “I wish it would stop raining.”
This would explain why “would” is used with the bothersome examples given above “I wish she would stop crying” (to stop doing something is an action), “I wish they would leave me alone” (action)... but “I wish they weren’t so mean” (state/description, and I wish it were the contrary of what it is)... “I wish it were warmer today” (same explanation).
This may not capture 100% of the possibilities/differences (I wish it would be warmer here in the future, wouldn’t be explained by this, but if I’m being honest, that sentence... while I wouldn’t interrupt somebody who said it to make a big deal out of it... doesn’t sound that great to me either), but it’s the most accurate and reliable distinction I have come up with to understand my own usage(s).
To drive my point home, consider:
a) I wish he were my friend.
vs
b) I wish he would be my friend.
In (a), being my friend is a state (he is, or he isn’t, and I am wishing for the contrary... in this case, he isn’t and I wish he were); but in (b), I’m turning it into an action “start being my friend” / “become my friend” / “make the decision to befriend me”, so the use of “would be” works... but on the surface (and even semantically), the difference would seem subtle, unrecognizable, or nonexistent.
I hope somebody finds this helpful, and I also welcome friendly counterevidence to my points and/or explanations of dialectal differences.