All I see is Random and Choose. Is that really the only two?
I completely disagree that mixed Random is "nonsense." To begin with, this is exactly what the rules say to do, so why would that option be removed? And some prefer it this way, especially more experienced players. And an option shouldn't be removed because some given person does not like it.
Choose is good - that's how I play it in person. (Although that's not in the rules.)
But I do agree that all A and all B should exist as well. In a beginner game, it probably is good to use all A. Some people might prefer this, and therefore they are good options to have. Except for the suggestion for a beginner game, the rules don't say you can do this, but I agree that they probably thought we were all adults and could decide for ourselves how to do this.
Sometimes the site cannot house rule certain things based on whatever agreement they have with their license. But I kind of figure since the rules suggest A only for beginners, and since they did include Choose (not in the rules), that including all A and all B would probably be OK.