The word will has a lot of definitions as an auxiliary verb, but I can't pin down which definition it uses in sentences like the following:
- Even though the plot was awful, I'll admit that it was fun to watch.
- I'll concede that point, but what about my other argument?
- I will say, though, that I didn't hate the trip.
- Good effort, I'll give you that.
I find it hard to believe that will is being used to indicate future tense here because the quote has already been said and the speaker has no intention of saying it again at a later time.
For example, in "Even though the plot was awful, I'll admit that it was fun to watch," the words "fun to watch" have already been spoken with no intention of repeating them later.