Hard counters must be allowed
Without hard counters, champions fall into a disjointed web of binaries: those who can do their jobs, and those who can't. If a champion does their job well, they're perceived as OP. If a champion doesn't do their job adequately, they're perceived as garbage and unpickable (for good reason). For champions whose job is simple (like doing damage, or being a CC bot, or being a heal/shields bot), this paradigm is exacerbated tenfold. Furthermore, notice I said "disjointed web". That's because without a complex system of counters, checks, and balances, champions don't truly interact with each other on the balancing board.
If a champion cannot perform their given niche role well enough (for example, if Annie can't reliably Flash-stun-burst), there is absolutely no reason to pick them beyond aesthetic or character bias. They do not interact with the rest of the champion pool in any way. There are no champions whom Annie hard counters, nor any champions who can in turn counter her should she rise to prominence. Almost all the counterpicks in League of Legends are soft counterpicks made rapidly meaningless should there be a shift in numbers. There are, at best, vague synergies (ex Lulu's E synergising with AA-heavy ADC's) and counter-points (ex Lee Sin being able to AoE deny stealth to Akali).
Without specific champion counters, we come to a cycle of “class counters”. We start with ADC's reigning supreme because of their kiting advantage (something that has diminished over the years with League's mobility creep problem; you can read more about that here.) To counter the ADC's you have assassins. To peel, tank, and duel the assassins, you have bruisers/off-tanks/fighters. To out-tank the bruisers, you have true tanks. To kite and shred the tanks, you return to ADC's. With the exception of assassin eras, the mid lane is usually relegated to wave-clearing control mages.
Every single era of LoL balance history has fallen within this cycle thus far. This cyclical imbalance is a direct result of the lack of hard counter champion picks in the game. It also makes the ban-pick phase of the game significantly less meaningful and cerebral. There is only a minimal shadow of the complex game of chess in which you attempt to counter-pick while avoiding counterpicks yourself. More often than not, ban-pick is a negotiating table and a game of chicken, the goal of which is to end up with the most OP's on your side.
Considering that this is part of Riot Games' business model—taking advantage of cyclical imbalance to push new skins and other purchasable content, I doubt that the problem will be fixed anytime soon. However, I urge the live balance to team to stop buying into the vision of a game that's balanced to be a homogeneous, centre-clustered mass.
This tired old charade of “balancing outliers” is little more than a joke at this point. Does nobody find it ridiculous beyond belief that the average champion pool over each entire season is around 35-45 champions out of approximately 130? Does it astound nobody that even a storied, tenured pro player like Dyrus only had 32 champions played in his entire professional career? A spectrum of counters, wherein each part has an equal opposite, is a more diverse and far superior system, and needs to be implemented for the long-term health of the balance in League of Legends.
That is unless, of course, Riot is still afraid of being seen as a DotA clone.