Do we even need Runes, Masteries, and levelling in general?
First of all, let's forget this whole argument of "something for new players to level up on", because given how many million people already play this game and how shitty the new player experience is in general, new players shouldn't be the main factor when it comes to questions of design that affect everyone.
Both Runes and Mastery systems are "relicts" of the olden days of League, when none even knew what the hell a proper "Moba" was and even that acronym was only known to those who played the - sometimes horribly - modded WC3 maps, although there the term Dota was more common. Actually, the entire levelling system was feels like it was just thrown in because of the fantasy nature of the game and to make sure newbies don't instantly jump into ranked.
However, that can be easily done with Champion Mastery. For ranked you need x champs and x mastery levels, of which Y need to be level 4 or 5. That'd make ranked access like "show me you can play at least so many champs good and some even better" instead of "sink X time and exp boosts into it". Basicially "you need to be this tall to ride the rollercoaster" instead of "you need to wait in line for this long". Which one of the two makes more sense is obvious here I think.
Runes are absolutely boring stat givers that take almost forever to grind games for, and on low-level, it might make up for some quite unfair lane matchups if someone has a Quint and 2 runes more than you and an free advantage over you in a game that is supposed to be fair. At the same time it makes balancing more complicated, as all base values and stuff have to take runes into consideration, making the earlygame kinda tricky to balance. Also, this results in one or two runepages being the "best suitable", kissing all promise of "individualizing your playstyle" goodbye.
And masteries... well, Riot TRIED to modernize them with keystones but... this game ALREADY suffers from damage creep, and adding a three-hit-lightening damage or stacking AD was not exactly a way of solving this. Reducing it would either mean making the keystones useless, or balance the champions around it. HOWEVER, that makes for a really shitty feel, as the champion is supposed to deliver the main empowerment fantasy in this game. Shifting any power from a champion to a source outside the champion is always a bad idea. Usable items or interactive objects like plants still work, but stats and masteries? Not working dude, not really.
"Stop dumbing down the game, go play heroes of the storm when you want that!" - that's something I heard already, but then again, what good is there in needless complexity? I mean, the basement of my hoarder-greataunt's house is extremly complex, but that doesn't change the fact that it is just complexly arranged junk and garbage with zero overall use or value.
And I'd happily trade some complexity for a more enjoyable and easier to balance game.