You have a few good ideas, but your execution is flawed.
Champion choice and items play a factor in who is victorious in different situations and they should. But they should be just that... FACTORS. As in... data points which contribute to a the final outcome and influence it to a certain degree. However, they should not be the only or even necessarily primary determining factor in deciding the outcome.
The primary factor should be a player's skill. Secondarily should be itemization and champions - with champions honestly being a distant 3rd assuming they are being played in their proper role. Putting priorities in this order creates the greatest emphasis on actual skill and strategy and leads to the most rewarding/fun gameplay possible.
But... in rock paper scissors, you blindly pick and win or lose based on which of the 3 you picked. Isn't that like champ select and therefore champ choice being the primary factor perfectly ok? No. In rock paper scissors, it is fine for your blind pick to determine the outcome because the other person must also blindly pick and so you are measuring your reasoning/deductive or pure chance skills (depending on if best of 1 or several matches) rather than determining who is the best "rock" or "scissors" player. Whereas in league you are essentially determining who is the best rock player and oh... they also have to hope 4 other people on their team are also the best "rock" players too. You see... one person has an innate advantage of counter-pick in league. So making champion counter-picking the PRIMARY factor in the outcome of a match leaves one side at an innate disadvantage. This can be somewhat overcome with team coordination and pre-planning in champ select, but it still exists. So there's fallacy 1 destroyed - champion select is not in fact true strategy which can/should be used as a PRIMARY determining factor in the outcome of a lol match. It can play a part, but should not be the MAIN part.
Next let's tackle itemization. So the predictable argument here in your favor goes something like... a darius top building full attack speed shouldn't beat a fiora top building standard items. To which I'd largely say... yes. Provided skill matchup is anywhere close to equal, the darius might cheese a kill or two early, but then get wrecked by fiora and should lose all subsequent 1v1's after a certain point... probably 2-3 items. But now, I offer you the flip side of the coin to that type of scenario. I'm playing jax and I built essence reaver cuz it's op on him. I'm vs darius. Now if I play my cards right, I outscale at 2+ items and can beat him pretty easily... snowballing myself ahead and becoming unbeatable. But let's say I don't understand the purpose of essence reaver so I essentially waste the passive of the item - which is what makes it so good for jax (keeping his e up non-stop if you pop ult before using e). I also fail to land my stuns on darius, waste my empowered aa's on minions most of the time, have poor mana usage, and never dodge a single darius q... so he heals every time he uses q. In that type of scenario the jax should lose even though he is jax (who beats darius; counterpick - which we destroyed in rock paper scissors scenario) and even though I have better 1v1 items. Arguing jax should lose here is no different than arguing that the darius should lose to the fiora we talked about earlier.
So if we look at that last discovery closely... we realize that what we WANT as the ultimate determining factor (the PRIMARY factor/data points) is... skill. Skill in 1v1 micro and macro. Skill in teamfights and skirmishes. Actual knowledge and tactics which a player uses and the skill and speed with which they input their desires into the keyboard and mouse to affect what their character does onscreen. The decisions they make about pushing or freezing... retreating, grouping, splitting, rotating... etc. This is what should be the primary determining factor and therefore, people CAN BE (not always are... but can be) 100% validated in complaining about strategy while simultaneously criticizing counterpicks and itemization. What they are really complaining about (if it is a valid complaint) is that itemization or champion select has overtaken true skill and in-match strategy as the primary determining factor. I.E. "I win because I'm playing jax" or "I win because I have spectre's cowl" regardless of how poorly I play compared to my opponent(s). And if that is indeed the reason for them complaining, then they are indeed justified in doing so. Because again... this isn't rock paper scissors or the lottery. This is league and it is supposed to be about the best individuals and the best teamwork determining the outcome.