Key Fragments for F2P Champs

I don't play league enough to get the keys I need for the chests I have (I have 5 chests right now 0 key fragments). I played primarily jg and support so far but I wanted to start branching out. So today I played a couple Ezreal games (Free to play this week) and I wasn't able to get any chests or fragments at the end. I saw this before but didn't really realize it was a problem until I wanted to play different champs and try them out before buying them. With 5 chests and limited amount of time to actually play the game I found myself not wanting to play F2P champs and instead playing the same role and playing the same champ over and over again. This makes the game hella monotonous and I think needs to be changed. I understand the not being able to earn the champion's specific chest but key fragments aren't champion specific. So I guess I'm just not understanding why you cant earn key fragments with F2P champions and would like some clarification as to the reasoning behind this...

or better yet allow players to earn key fragments with F2P. [slayer-pantheon-thumbs]