Wouldn't it be interesting to try to pin down the difference between those two phrases: I may go and I might go?

If I may go indicates a freedom to choose (it is possible that I shall go, but I have not yet decided) does that mean I might go is used where I have no control over whether I go or not (I will go if circumstances permit)?

Or is it the other way round?

Another possibility is that I may go indicates that I am permitted to go while I might go shows I am able to go.

But isn't that what can is for?

These are shades of meaning that I suggest could have brought about the different usages, but I am only offering them as ideas. My dictionary does not confirm that these differences in meaning - or any other - are conveyed by differentiating may from might in the present tense, and I believe that many modal verbs manage to convey such fine distinctions without pressing the past tense form into the service of the present tense.

When you examine the possibilities I have suggested above, I believe you have to conclude that might in the present tense is incorrect in any sense and may is perfectly able to convey all the subtleties required of it by the speaker without assistance.