I doubt 5e will go the BECMI route.
I suspect that adopting this as the only model for distributing the rules would be a step too far for gamers who are by now used to the traditional hardback book model. And I doubt WotC would risk having two overlapping presentations for the same game - they would fear competing with themselves.
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Slimming down the core ruleset (ideally so that the PHB/DMG/MM becomes a single book of about the size and scope of the SWSE core rulebook) would also be a good idea. Make the game easy to get into, easy to start playing, and immediately fun, and then add the expansions for the people who want them.
I agree. I think the BECMI route by itself, would probably be very popular in some quarters, but ultimately not overall. You can see this by the outrage at not having a bard class in 4E PHB 1, for example.
However, starter book that is self contained + PHB, DMG, and MM--really only has one objection if done well: The people that used to buy the core three now will want the core four. Let's see. I get the starter "book" (even if in a boxed set instead of a book), which has the main rules, and enough classes, races, monsters, and treasure to let me play for awhile. Now suddenly the old core three books aren't having to provide all that. They provide expansion and options to that core. It enriches what they can provide.
In trade for your typical player now wanting at least four books, you get two very good things: A starter set that is integrated into the ruleset, not tacked on. PHB, DMG, and MM really focused on what it says on the cover. And if done right, the folks in the middle can be choosy and/or gradual even so. Get the starter set, and then if you mainly play, maybe the PHB. Or if you want to run a BECMI type game and are happy with the starter set, but want more monsters, get the MM too.
This only works if the starter set is more of a "core basic" set, though.