You can achieve mastery level 6 & 7 without opening a single chest, and without using a single Key. Without using your credit card, and without spending RP.
You DO need to play enough games to earn IP which you buy champion shards with. These champion shards are disenchanted into blue essence. Not once are you required to spend money, use a key, or open a chest.
This is how the system has been designed since the beginning and here is the original announcement when Mastery levels 6 & 7 both came out to the Live Servers, in the Patch Notes under the tab "Champion Mastery"
http://na.leagueoflegends.com/en/news/game-updates/patch/patch-610-notes#patch-champion-mastery
You'll notice it explained that in this two system part of Participation and Performance,
The Performance: is the result of the S ratings
&
The Participation: is the result of collecting the IP needed to buy champion shards...
Champion shards = Blue Essence....
As well as other methods of obtaining blue essence
(and these alternative methods favor people in situations that don't apply to you; and they aren't being forced onto you anyways), and even for these people who prefer these alternative methods, they don't have to pay to use them!
Here is another follow up to that post (as the post said there would be) specifically on this topic where it reinstates just that:
That you don't need chests or keys, or credit cards to get to mastery level 6 or 7.
http://na.leagueoflegends.com/en/news/game-updates/features/champion-mastery-levels-6-and-7-live-now
Please take responsibility for your wallet; do not blame Riot.