Key Fragments

I've got a problem. When Hextech Crafting dropped, I was hyped. Who doesn't want some free skins? But it's a bit harder than you might think. I own 69 of the 130 or so champs. Not only are key fragment drops not very frequent, but when you would get one but do not own the champion, here's the message you get:

"You must own the champion in order to earn its mastery chest or key fragments."

Now I'm not complaining about their drop rates, I play enough to get them and not have a huge pool leftover. Generally I'm always short key fragments. But as of the past 48 hours or so, I have gotten this message 10, I repeat, 10, times. Why? Because I've been playing a ton of One for All and I want to play champs I don't have. Now here's the complaining part. In addition to getting this message 10 times in the past 48 (if not 24) hours, I've gotten 3 times in a row after my past 3 games. I have 4 chests sitting in my inventory, waiting to be opened. However, since I don't own the champions I'm playing with, I'm not getting key fragments. And when I am playing with champions I own, I'm not getting the chance to obtain key fragments. So, I legitimately cannot obtain key fragments unless I continuously play only the champs I own. Due to my growing frustration with the fact that you must own the champion to get the key fragment, I'm reaching out to the community to help me find a solution to this huge problem. I'm grinding this game, playing over 10, 15, on occasion 20 or more games on a Saturday or Sunday, and obtaining 0 key fragments. Now I'm not asking to be able to pool key fragments or anything, but this is really getting to me. My proposition to part of the solution is to of course, make it possible to obtain key fragments from games even if you don't own the champion. Maybe make it much less likely, a third of the chance or whatever, but I would really like it to be possible. If there is anything else you guys would like to add to it to help fix this small but very annoying problem, please do. Thanks!

P.S. I understand it's a system which gives free skins, but this is still a very frustrating message to see.

TL;DR: I can't get key fragments because I don't own champs and it's frustrating beyond belief. I'm looking for a solution to change this, please help! Probably would help to read a bit of it to get what exactly I mean though...