leverage
If we're all on basic income, we no longer have any leverage if our "wages" are reduced. The ruling classes can decide to drop the amount we earn, and there's not much we can do about it. Sure, we can "vote", but we can't strike, which is a far more powerful way to fight against pay decreases.
education
the main driving force behind education is the need for employment. of course plenty of people seek education purely for their own fulfilment, and we imagine with the free time that will come with joblessness, more people will do this. but we'll almost certainly see a drop in the number of young people attending college, since there's no "need". with less people in college, the overall level of education around the world will drop.