In theory, the home play category (playing through the main arc adventures Hoard of the Dragon Queen and Rise of Tiamat, and/or the Starter Set's Lost Mine of Phandelver) is pretty robust. The Starter Set is through level 5, while the other two are levels 1-15. That's a lot of play and all official.
In practice, many will want to be part of Expeditions. And for that, there is no home play. You could play the other adventures and then move over, but you might level out of many of the games. It isn't clear that you could play the Starter Set and then go to Gen Con (assuming you could play it all fast enough) and still play the Gen Con adventures as a 5th level PC. Maybe you can?
How levels work and what transitions exist could be significant. If players can easily play one adventure (say, Encounters) and transition to another (say, HotDQ), that really encourages continued play. But if things are one way (can't play at Gen Con and then play the Starter Set), those barriers can make play less rewarding. (If I can play Encounters, HotDQ, Expeditions, etc. all with one character then I'm really able to get immersed). The number of characters I have to create is also a potential barrier. In LFR gamers had so many PCs that they lost touch with what their characters had done, if not the basic personalities and goals of those PCs.
I'm not saying AL should allow complete interconnected play. It gets complicated to try to create many different experiences and have them all work together... not to mention the story narrative. Every organized play program has to choose its limits because you can't do everything. It will be interesting to see how these factors influence and reward play.
I agree that having public spaces qualify would greatly expand the options. I bet a lot of people could spread DnD to book stores, cafes, schools, and other areas. That could be very good for the game... though it might not be what Wizards wants in terms of a program to encourage store revenue and store WPN membership!