The Core Problem with League
They took the whole concept of "classes" and sorta threw it out the window so they could have full creative freedom. The problem with this..is classes still exist naturally, either riot likes it or not and those classes are the following if you don't get into the complicated sub classes.
Mage Assassin Marksman Tank Enchanter/Support Duelists/Bruisers
Now for the sake of discussion and debate let us all be clear on what each class is, in a short and brief description.
Mages: Long ranged spell casters, who lack mobility but make up for it in either the form of utility spells or strong burst, many times consisting of both.

Assassin: Highly mobile, combo focused characters, that specialize in jumping onto a target, and bursting them down with a combo, they rely heavily on mobility and busty combos, but lack heavily in defense and utility.

Marksman: Characters that focus heavily on selecting a single target and gunning them down with superior auto attacks, they rely heavily on attack speed stats and powerful autos to allow them to take down tankier opponents that normal mages and assassins can not deal with. Some marksman have utiltiy and focus on spell casting, but even than, they always weave heavily in autos with a prioritization on positioning and kiting mechanics.

Tank: These characters many times will lack mobility and damage stats, but will make up for it in pure raw defensive stats, and a entire toolkit dedicated towards cc or protecting allies with their natural tankiness. They are the front line of your team and meant to soak the damage and give the enemy team no choice but to focus them.

Enchanter/Support: Enchanters are characters who lack just about everything, they have no damage, no mobility, and no defensive stats, but what they are given to make up for this, is a entire toolkit dedicated to utility, weakening opponents, and protecting their teammates. They do this through shields, auto attack steroids, slows and deflection abilities.

Duelists/Bruisers: The Duelist class is a class that specilizes in being neithier to tanky, nor to damage focused, because of how this mathmatically works, the duelists are the ideal class for one v one scenarios, and rely heavily off mechanics and understanding in how to one v one someone. They are given elements of just about every class, but are not to opressive in any of those elements. The jack of all traits class.

So when we keep it to five classes the game makes alot of sense, all five of these class have clear roles and designs in how they should function. However where things get complicated is when you get into the hybrid classes.
Bruisers Divers Juggernauts Mage assasins Mage Duelists Caster Marksman Assassin Marksman
To avoid making this topic stupidly long we won't get into to much description about these classes. But basically they are classes that are suppose to take elements from other classes and fuse them together, while also gaining the weakness of those classes. But the result is often that they lack a weakness and thus as a end result are filled with over loaded toolkits that take forever to balance. Prime examples
are marksman and mages
Assasins and mages, ekko also having duelist elements
lucian is a fusion of a mage and a marksman while having mobility of aassassin, while twitch has the stealth and damage of assassin in the form of a marksman
But i'm not even just talking about that. It also goes down to how riot does the stats/grading in when creating champions. If i was to make a scale on how I would grade a champion it would look like this.
Mobility DPS Burst Tankiness Utility
DPS being how consistant they can do damage per second, Burst being how fast they can one shot someone. So if I was to grade each class out of 5 stars in this category it would be.
Assassins Mob:5 DPS:2.5 Burst:5 Tankiness:0 Utility:0
Mage Mob:0 DPS:2.5 Burst:5 Tankiness:0 Utility:3.5
Marksman Mob:2.5 DPS:5 Burst: 3.5-4 Tankiness:0 Utility:1-2
Enchanters Mob:0 Dps:0 Burst:0 Tankiness:2 Utility:6
Tanks Mob:2 DPS:1 Burst:0 Tankiness:5 Utility:4
Duelists Mob:2.5 DPS:3 Burst:3 Tankiness:2.5 Utility:2.5
That's honestly how it should work but instead we get this..towards specifically towards stuff like tanks and marksman
HOW RIOT DOES IT
Tanks Mob:2 DPS:5 Burst:5 Tankiness:10 Utility:5
Marksman Mob: 3 DPS:6 Burst:6 Tankiness:3 Utility:3
So really in my first opinion the core problem just simply goes down to, they give classes stats they should not have, thus making them break the identity they should have, thus creating a imbalanced game.