Wall of text alert.
I'm rather new to League and for me I have to say one of the most...frustrating parts to try to understand is the item shop. Especially since I've always been the kind of person who likes to create my own builds because I find it fun, but that doesn't really seem to work because you either use the recommended build or guide builds.
It depends, some champs do have alternate builds. Take Sion for instance. You could build him full tank (the meta build), full AD or full AP. He has scalings to support all three. Or even Kai'Sa. You can build her for either on hit (items like BotRK and Guinsoo's), AP on hit (items like Nashor's Tooth) and attack speed, full AP and magic pen, or crit and attack speed as her kit has scalings to support all those builds separately.
There are plenty of champs that have off meta builds that work (one of my favourites is full AD/Lethality Jarvan IV).
With some champs it would be impossible as they do not have the scalings nor do they synergise with an off meta build. For example, Twitch has an AP scaling on his E, building him full AP would be useless because, his E deals physical damage (making magic pen useless) and because he has no other AP scaling on his kit.
Another reason is because the result would be toxic for gameplay. For example not that long ago some assassins built tank items (Ekko, Fizz and Akali), which meant the had the damage and mobility of an assassin with the survivability of a tank which breaks their champion archetype of being squishy damage dealers and is overall unhealthy and toxic.
Which made me wonder what this game would be like without the item shop and how champions would be balanced differently to survive without it. Obviously the item shop gives for example speed buffs, but I wonder if this could not just be built into champs as the level instead of relying on items to do it. I mean obviously their is no reason to buy a attack speed + crit bonus to a slow character who is mostly a tank and I've been told not to buy armor for Xayah for example - which raises the point.
Whats the point of buying armor for xayah if it doesn't suit her? Or rather why even give the option if everybody says build up her speed, ect.
Honestly, the game would probably be a shittier version of HotS.
You can buy armour on Xayah but that would come from either Guardian Angel or Ninja Tabis. Building other armour items (IE tank items) would be ineffective as she needs to buy damage items to deal it as she's designed to deal nothing but damage like all other marksmen and to deal so much damage she gives up defence.
As a new player the item shop seems kinda like a relic from Warcraft 3 or Kings Bounty where the focus is more on long term rgp elements that belong in a strategy game.
Basically, yes. MOBAs found their roots from the RTS genre. League and DotA 2 are based on DotA Allstars, which is based on the original Defence of the Ancients map for Warcraft III, which is based on a map for the original Starcraft game called Aeon of Strife.
Aeon of Strife and Defence of the Ancients basically kicked off the MOBA genre.