I have done some thinking about this over the last few days. It seems to me that there are simply people who want different things out of this, so I want to go back to Marcin's division of players into categories based on what they are looking for.
1) Collector Players -- people who primarily enjoy the PROCESS of collecting. Since they enjoy the process, it is less likely to feel like a grind for them, although they will still want to feel like they are making regular progress. In my real life experience, these players really enjoy opening boosters. Also collecting needs to feel like it has some sort of meaning, so it would be nice to attach certain tournaments or events to your collected cards. If it is too easy to collect everything, these players will lose interest, although the existence of foils does help this somewhat.
2) Competitive Players -- people who primarily enjoy thinking about what will work best in the game, both in terms of tactics and in terms of deck construction. They enjoy competitive play since it really highlights this kind of thinking, so leagues and tournaments are good attractions for them. However, they are easily put off by the collecting process as that is not what they want to put their time and energy into. (In real life, they put money in instead; the usual argument being that the entertainment value per dollar out of a few boxes of boosters is much better than what you spend going to a movie or a nightclub.)
3) Casual Players -- people who just want to play the game. They will enjoy leagues, and they will enjoy tournaments too provided there is not too much of a barrier to entry -- they don't want to take forever to get a deck together. They may also enjoy collecting, again provided the pace is brisk.
4) Testing Players -- people who currently play in real life and use the site primarily to test out decks. They are pretty easily satisfied by casual play.
As Marcin noted before, Casual games are enough to satisfy group #4, and are also appreciated by the other groups. League play is appreciated, I think, by all of the groups. Group #1 wants to be able to collect cards and for that to be meaningful, they need to have tournaments they can use those cards in. Group #3 may also enjoy collecting cards. Group #2, however, wants to be able to play competitively without collecting, and some portion of group #3 would prefer that as well.
Additionally, it seems to me that any proposal for collecting cards will have a hard time satisfying groups #2 and #3. For example, Marcin said above:
So, to give an idea of how big the card acquiring rate I have in mind is. If you had a FotR block decklist, then with enough effort (playing leagues and doing quite-well in them), and being smart (planning and buying cards from merchant in advance) it should take you 2 months (less than a season) to acquire all the cards for that one deck.
This means that to put together one constructed deck the way you want, it would require deciding in advance what you want, watching the merchant, and playing 80 league games (in formats you may or may not enjoy) all over a period of two months. I can see how some people might really enjoy this process, but I think it is also easy to see how much of a grind this would feel like for someone who is not interested in collecting. Some people will enjoy it, some people will hate it.
THEREFORE, my suggestion is -- rather than trying to make one solution work for both collectors and competitive players -- simply run two types of constructed tournaments. Run Collector Tournaments where you must own all the cards in your deck, and run Open Tournaments where you can use any cards that are in the format, regardless of ownership. I think this is the easiest way to make everyone happy.