"tying it into something that requires money" .... The only thing that it "requires" is that you play. I don't think you understand what a requirement is. You can now get things for free via a method that did NOT exist 6 months ago, or a year ago, or two years ago, or in beta, or at any point in the game's life. Riot Games has no reason to give you anything for free. They don't owe you anything. You play a free game. This is based far more around skill than money, but they also want it to be somewhat exclusive, unlike tier 5 which you can get after 20 good games. I have tier 5 on around 10 champions. 5 of them I suck at. i just happened to play them enough to get tier 5. I've even gotten an S on a champion or two that I suck at.
I realize that using my personal experience to back up my own point is bad etiquette, so let's look at it another way. If you play 2 games a day, then you likely get your new chests as soon as they are available, or 1/week. It may be less likely if the person in question never ever plays with a group, but I find that unlikely. Now the only hinge is keys. According to Socrates on reddit, the average player earns 4 keys (12 fragment) in a month. https://www.reddit.com/r/leagueoflegends/comments/476v2l/what_i_learned_about_hextech_crafting_in_10_days/d0apufq
So the average player can open 4 chests a month. If getting any given item from hextech crafting is equally likely, which I will assume because it is more beneficial to you than me, and I can't find any data on the distribution, then about 1/5 of the time you will get a champ shard, on average worth 300 essence, meaning that on average, if you can all of your champ shards for essence, it will take near 2 months to get the essence needed. However, I have 6 champ shards, and I've only bought 1 chest since hextech crafting began, which means that it's probably NOT equally likely to get any item, but that's merely anecdotal.
In summation, the average player, without purchasing anything should be able to rank a champion past mastery level 5 on average 2 times every 3 months or so, barring they randomly happen to get a shard for the desired champion, for completely free.
Does this still feel more like a money grab more than anything else that it could be?