Why? Perhaps that is not the norm in the MU.
In the MU, I actually think they'd be more likely to let people fend for themselves before they turn 18. So if it were different from our society, I think the difference (though I know we don't know this) would be that they consider or at least treat people like adults earlier.
By which point (whenever that would be) Georgiou would tell Burnham, "There are some things I regret, Michael, things I could've done better, but I did the best I could and now you're on your own."
Or perhaps Georgiou didn't feel that Michael needed a father figure and even if she did think that, she might have thought that she was strong enough/good enough to be both.
At first, probably. But like she said, she eventually realized Burnham was missing a father figure in her life.