Of course, students who really aren't paying any attention are likely to fail courses and quickly fall below enrollment standards, so there's already a fail-safe here.
On the other hand, restricting access to technology is a draconian measure that can have unintended consequences (many outlined throughout this discussion).
The reality is, schools don't want students to fail out. There are plenty of altruistic and selfish reasons for this, but it's in their best interest for their students to succeed. There's no reason that schools can't inform students about the dangers of distractions during class time without setting up new rules.
Professors who enact bans, rather than working to improve their teaching style are doing a disservice to their students, schools, and subject areas. The college experience should be more broad that simply "learn what I tell you about this subject" and part of that lesson should be helping to find your personal learning style. As adults, students also have the option to make up their own minds about what information is useful, accurate, or ignorable. Professors should be doing their best to explain why their information is worthy of attention and acceptance.
Let the natural incentive structure demonstrate which learning methods work best and more power to the students who can play video games in class while still mastering the material.