We can compare it to other games, why not.
Let's see the two most popular competition, DotA and HotS:
In HotS you don't have items or prematch settings (like runes, masteries, whatever) but you have unique talent trees for every single hero, giving you several balanced and valid build routes on all of them. And they are even unique.
In DotA you again don't have any prematch settings but, despite you have an even more complicated item system with three different shops on the map and such, you have unique talent trees for every hero what you can raise as you level up in-match and you also have three basic attributes, Strength, Agility, Intelligence, what you can use to customise your hero and playstyle.
In LoL you have none of the above but you have some prematch settings to fine-tune your champ. And the idea itself is okay, as otherwise you would have way less diversity. Imo, despite it was far from perfectly balanced, the old runes+masteries did this job pretty well, with giving mostly passive bonuses and stats. Because that's why a system like this exists and not to give stronger abilities what your actual champ abilities...
I think with the new runes Riot made a mistake as they misunderstood what the community meant by "more meaningful options". As they supposed to give more valid build variety and not to give overpowered and overcomplicated new runes/masteries but mostly tuned them to pure damage output, making the window of options even more narrow.
And the other, very serious issue with both the old and new systems, what you can't find at the competition above, that these features - as they're actual gameplay features with a significant impact - should be perfectly free and accessable the very same way for every single player. No payed or otherwise unlocked runes and rune pages or any BS like these. They seriously should take a deep breath and cut this crap MMO-ish grindy feature once and for all.
So, imo, the problem isn't with the very idea of runes or masteries but the way Riot designs them and the way they include it in their business model.