Android already has side loading, and Epic tried and failed to get a third party store going. I highly doubt this bill will do anything unless it mandates that Google can't mandate Google Play Store as a condition of receiving development support.
F-Droid is great for hackers- a niche subset. Chinese app stores are a special case because of legal and political separation. How successful are Amazon or Samsung's app stores, and do they actually host any popular apps that users can't get on the Play Store?