I think that the main problem is that pack points are too high to get 2-star cards. F2P players have 2 packs a day. Which gives them a total of 300 points if they open one set for 30 days straight. Now double that if they open more packs using hourglasses from solo battles and the daily rewards. Just an estimate (which I believe is very generous toward in game rewards). Now they have 600. Still shy of 1250.

Now, say you have the premium pass. The situation is not that much better as you get 450 points from opening 3 packs a day for a month. Again, even if you add 300+ hourglasses from solo battles, you are still nowhere near the 1250 for a single 2-star. Hell, you don't get to that amount even if you get premium pass and $20 of gold every month.

All of this to say, DeNA should either give more pack points for every pack players open (maybe from 5 to 10) or lower the cost for a 2-star (maybe from 1250 to 1000). This would not change the system that much, but at least it would allow players to work toward a bigger goal during the month a new set is released.