Disclaimer : what is going to follow is my opinion as a player that played in leagues and as someone who follows them, not as a league organizer.
The begginer's league "problem" of not being for begginers only. Isn't (in my opinion) a problem. The reason is that organized pvp is tough. Getting a name is tough. Winning a tournament is tough, winning an event, or winning war, or winning trials, too. The main reason for this is that when you play organized pvp for the first time, you get to face people which have played the game for 1 or 2 years, which know a lot of techniques, a lot of deck types, who have a lot of mindreading capacity. They know how to test decks, what is going to work against what, what this ban for this tournament is going to change, how people'll react in general, and how to react to that. In short, they have experience.
Originally, though, these people were new to organised pvp. How did they get experience? By playing versus other people who have played the game for longer than they have, and who have the experience themselves.
When i started leagues, i was really a noob. If i recall correctly, i started BL in the last month of season 2/2011 (there was a special allowance on that season). I played versus people like TStar, whose level was way above me. And that wasn't frustating, because i learnt, and i had fun, and T had fun (search for the AI0 deck on the forums to see what i mean by fun). If i had to face some people on the same level as me, i feel i would have learnt way slower than i did. And hence been unable to have any effectivity in tournaments, trials, war, ect.
A bit of a fastforward. Season 1/2012. I've got a lot of experience in the two season before, and am quite happily sitting on the top of the rankings of BL. My feeling when i saw new people wasn't "Hurr durr yay points", but more "How can i teach them the basics?". And boy, there were results. For example, regen2k9 made the prototype of the monolight that eventually became incredibly strong in BL. Cheesy111 started in that season too, and both placed in the top 6 in both that league and the 2/2012 one.
The point i'm trying to make is that begginer's league toughens up recentlytookorganisedpvp people. Having a league only composed of them would make BL => Other pvp events become a very wide jump. And also cuts a road to get to know people, socialise with the community.