It might work, eventually, for organizations with very simple needs - they need a logo just to seem like a real business. But notice how none of these logos communicate much.
I have to say, logos are not where I would expect AI to triumph in the next little while.
Logos work when there are subtle resonances between what humans know, how they perceive things, and the wealth of information humans accumulate over a lifetime of looking at things. Not to mention, how one uses all these factors to distinguish oneself from peers.
The history of computers has often proven pronouncements like mine wrong - but usually the computer is used to do something different rather than replace the subtlety a human can bring. I still find it hard to see where the space is between “I made us a logo in Word with Papyrus” and a proper design process.