I suspect your premise about gaining more points for winning than losing is slightly off. Generally speaking, once your point level stabilizes due to finding your actual skill level, your points will remain the same relative to others playing the game if you don't get any better/worse.
However, the total number of points everyone has will trend upward due to the Bonus Pool. This does mean it rewards playing more often, but only to a certain extent in a certain time period (a few games per week, I suspect). Once you've exhausted your bonus pool, your ranking points will again more-or-less stabilize based on your skill.
One of the reasons this was done was to encourage people to actually play the game. Since everyone's points are constantly going up, you have to play to keep up with your peers. If this artificial inflation of points due to the bonus pool wasn't in place, the player at the very top would - in theory - not have much reason to play; he's the best and his points will stay the highest until someone usurps him. This way, he has to keep playing to maintain his status. As with any fair matchmaking system, the more people playing, the better, and I think Blizzard is trying to encourage more people to play.
However, none of this is cut and dry so there's no one reason for any of these decisions; likewise it's not at all obvious whether this system is superior to the traditional ranking system you mention.
That said, here are some good articles on the subject:
Note also that the points you see displayed and used for your ranking may be separate from the underlying statistic used for matching you up against other players. The two stats should converge on relatively the same thing, but the Bonus Pool adds the extra incentive to play more often.
So hiding your actual ELO Style ranking was a move to prevent smurfing as well as direct comparison between people in different divisions. The ultimate goal of a division is to prevent you from being rank #1,000,000 (my current MW2 Rank). However, if your ELO rank was displayed it would undermine this goal.
Because ranking within a division is still important, Blizzard also introduced a points system so that people could be ranked with in a single division. This number is visible so that people can use it for personal goals (and to know why so and so is above them despite a win/loss number).
Finally, your Hidden rank is actually an estimate which is used to determine who your opponents are and what league to place you in. As points are only relevant to a given league, it is necessary to have such a rank to allow for placement during league advancement.
Best Answer
Divisions are just a segment of a League, they don't really mean anything at all. You will play with people from many different divisions while you are playing.
When you qualify for a league, you are randomly placed into whatever division is currently being filled.
All the divisions do is break the people up into groups of around 100, and give you a rank to strive for. You shouldn't ever change division until you change league. And your league will change as you do well or poorly in your current league.
They poll your skill randomly and decide weather or not to bump you one way or the other.
You can on occasion have matches against people from other leagues, to test your skill level.
Lots more info here: http://starcraft.wikia.com/wiki/League_%28StarCraft_II%29