Why do you need materials to get to the next mastery levels?

Yeah I got 3 lvl 7 veigar shards and 400 blue essence.

Because they want you to spend 1700 IP on the random champ shard to convert to essence.

cuz RITO said so

its their game its how the designed it

So, this is just me hazarding a guess here, but, my guess is: Reaching Mastery Rank 6 and Mastery Rank 7 needs to feel more like a personal achievement. It's not something you can throw out like, say, "I just hit MR5 as Renekton, I'm awesome" - because MR5 is just a matter of playing enough games as a champion. With MR6 and 7 requiring Hextech Crafting, it helps gate that feeling behind an actual dedication and reward, and, what I think is the most appealing part of using Hextech Crafting for reaching MR6/7, is...

It is probably one of the most ceremonial things you can do in League. (although it is equally as ceremonial as opening a regular hextech chest or reforging shards into permanents, but I digress.)

Plus, it gives players with an inane amount of Influence Points and nothing to buy with them a reason to buy something with them - Champion Shards. That was actually one of the primary selling points of the Champion tokens - being able to achieve MR6-7 without having to burn too much time or money on Hextech Chests.

But, I am neither a psychologist nor a member of Riot, so do take my first two paragraphs with a grain of salt.

I think you mean Essence not Material.