Learn English – Changing the meaning of sentence by grammar

"Wish" is used to express regret and that something isn't as you would like it to be.

Ex. I wish I knew her number. (= I don't)

Ex. I wish I didn't have to go to school. (= I do)

Even the example that you found in the book:

I wish the weather would be nice this weekend. 

implies that the speaker would like it to be, but the speaker doesn't expect this to happen.

Especially,

I wish the weather would get better. I'm tired of being inside all the time.

tells us that the speaker wants something to change, but it is unlikely to happen.

There is one instance though when the use of "wish" can mean "open possibility," to borrow the OP's words.

wish + somebody + something

Ex. I wish you luck.

Ex. I wish you success.

But you cannot wish that something happens. You still need to use "hope":

Ex. I hope you get a high score.

When the context is absolute ("as good as," meaning "the best"), then the present tense is used to indicate permanence. "The best" is permanent because it is never better or worse; it always is what it is. There is no future or past tense for an absolute condition, because an absolute condition is considered not to change.

So your confusion comes from this: You are thinking of some thing or some object as "becoming" something, but the structure of the phrase does not refer to any particular thing: it refers to the absolute state. The absolute state of "bestness" is a concept that never changes, so it is referred to in the present tense.

Here are two more ways of looking at it: 1. You were trying to correlate "get" with "become," and that has some validity, but it's hard to see the correlation when you just correlate the present tenses. Try taking your translation ("it will not get any better") and put "become" in there, and that should make sense to you ("it will not become any better"). 2. Consider that there could be another word in the phrase "as good as it gets". It could say "as good as it ever gets." Ever is implied; we don't need it, but if you put it back in, doesn't that make more sense to you?