Perhaps I think that the "disconnection" that many people have with "why do I have to start at level 3??!!?" could be fixed simply by starting again the level numbering at each tier.
So you'd have:
Apprentice 1, Apprentice 2 (who knows, maybe Apprentice 3...)
Then you make the grade and start again as an Adventurer
Adventurer 1, Adventurer 2, up to Adventurer 17 or 20 or whatever.
This I think can also solve a little problem that may seem insignificant, but actually I don't think it is.
When they sell adventure modules, putting on the cover "for level 1-3" has a big different psychological impact than writing "for level 3-6". The former instantly marks the adventure ad introductory, does not turn away novice player to the 5ED game.
Mind, not novice players to roleplaying games in general, that's what Apprentice tier adventures, if any, should be targeted. I'm talking about Adventurer tier adventure modules, which should be the bulk of the published modules.