"I wish I would wake up early"

Is this sentence correct?

I wish I would wake up early

Some grammar rules say that would shouldn't be used when its subject is the same as wish subject. It ‘would be illogical’, the rule says.

I came across this sentence which seems to break the rule. What is the reason?

We can use wish + subject + past tense to express regret that a present situation is not how we want it:

I wish I had a car. = I don't have a car.

I wish I knew the answer. = I don't know the answer.

I wish I woke up early. = I don't wake up early.

We use wish + subject + would to express regret about an action that a third party is unwilling to perform.

I wish she would go home now. = I am sorry that she isn't willing to go home.

I wish he would get a haircut. = I am sorry that he refuses to get a haircut.

It would be strange to say:

I wish I would go home now

or

I wish I would get a haircut.

because I have the power to perform those actions if I want. This is why Thomson and Martinet in Practical English Grammar (p262) state:

The subject of wish cannot be the same as the subject of would as this would be illogical. We cannot therefore have I wish + I would.

The example sentence is somewhat different because the speaker is not expressing regret over a unwillingness to wake up early but over an inability to do so. In this case, I wish I would wake up early seems acceptable to me. But I prefer:

I wish I woke up early

or

I wish I could wake up early.

I disagree that "?I wish I would wake up early" is a good English sentence.

Here's what's wrong with it. Both wish and would let you describe an event that isn't real. You simply don't need "would" if you say "I wish I woke up early." A principle of pragmatics (the study of how we use context to communicate) is that we don't say things we don't need to say. So when you say "I wish I would wake up early" the listener immediately wonders why you needed the extra word. For me at least, it leads to a brief speculation that for some reason the speaker is not in control--trapped in a dream or something.