The first alternative app store has launched in the EU. The appropriately named altstore is focused on iOS only.
Words like “anyone” can distribute their apps conflicts with everything Apple states they stand for with terms like protection. Interestingly, the store is charging 1.5 Euros per year to cover “Apple's Core Technology Fee, payment processing, and server costs.”
Will we see uptake in the near future? Unlikely until the alt stores have enough apps and the user is given an option when they initially setup their phone or asked periodically. We have seen some uptake on the browser choices but we are years from traction here.