If we had adequate testing, and could quickly identify carriers, we could open schools. But we don't have the testing capability, and in the absence of a federally-driven push to get there, we won't (it's not profitable enough, I suspect)... although I'm sure that some states will attempt it, if only because the modern role of schools as day-care for kids whose parents both have to work to make ends meet. If the schools don't re-open, a lot of workers cannot go back to work, since stay-at-home parents are so rare now.
Schools are quickly developing distance-learning / tele-learning capabilities. These are, as of now, probably not a great substitute for in-class teaching (at least where teacher-student ratios are reasonable, and teachers are high quality)... and we lose some fairly important socialization skill learning. But that said, the distance learning techniques will improve - probably already are in a lot of districts.
Now, this means no extra-curriculars. No high school athletics. No football and basketball players angling for "college scholarships" (I use the words advisedly, since many/most of these kids aren't really interested in education...). A disruption of the major-college athletic pipeline.
Not that, in all honesty, I care much about this last. We may not end up with precisely the same professional athletic entertainers, but when the games resume, the rosters will be filled. If, along the way, some institutions of higher education discover that being minor-league football and basketball factories isn't central to their missions... I'm OK with that, too.