The 'random' button would interfere with their aggregate viewership tracking and recommendation algorithms. When the viewer appears to select a particular show to watch, you can have reasonable faith in the viewership numbers.

If the platform were to offer a random choice, the fact that the resulting view was not organic would need to be tracked separately. Conversely, you'd want a better way of figuring out whether the viewer was satisfied with the content after all. These problems require nontrivial effort.

Right now, things are much easier. The viewer always makes a choice, ostensibly a conscious choice, and all views factor into aggregate numbers that correlate with show popularity.