Mastery 6 and 7 is just a lame excuse to use champion essence
It doesn't make sense for it to work on an experience bar sort of system up until 5, then require weird random specific things to go to 6 and 7. Being lucky enough to get a specific champion shard(or having enough other shards to dump into essence) has absolutely nothing to do with getting better at a champion.
Seems to me this was only done to shoehorn a way to use champion essence into the game just so it's there.