In addition to what's already been said, I feel like my biggest problem is that they've gone overboard with the damage output of champs through masteries and items. Item variety is a great thing, it allows players to customize their experience and play a champion to their brand of playstyle. It may not always be the most effective way to play said champ, but in most cases, a player who is well-experienced in their champion can still make a pretty decent game of a quirky build.
Back to the point, they've gone overboard with damage, and it's why you see tons of posts claiming that bot lane is the decider of game wins. In general, there aren't good ol' fashioned brawls like there were in early seasons. Has anyone else been around long enough to remember the original Twisted Treeline? League of Bruisers. That was quite literally the only thing you could play that lived long enough to withstand the long drawn-out battles that required planning and teamwork. You had fights that lasted long enough for some people to use their ultimate TWICE before the fight was over. Now people are able to engage a fight, button mash, and the other person is dead. There's no reaction time, no back and forth. Just BOOM, do WAY too much damage in 1 fell swoop and the fight's over. Follow the progression of items and you'll see what they've done.
Season 1- Heart of gold / Regrowth pendant / Force of Nature/ WOTA/ Malady/ DFG/ old Wit's End/ Mana Shroud
These were items that you could buy and use them for what they were; strategic advantages. They all came with drawbacks. (Heart of gold didn't build into anything. It was just a little bit of health, but you got gold in return for the inconvenience. Regrowth pendant gave no stats other than health regen.) These items slowed the pace of the game by lowering the overall amount of damage you did so that you had to focus more on strategy in terms of how much poke you could take, how long it takes to recover from them, and how long you can keep your opponent stalled to let your jungler get in place to help gank for you. You could quite literally do math in your head as to how much punishment you could take before it was time to back.
As to the other items I listed above, they were specialized. Hardly anyone besides Kog and Teemo used Malady because it was a strategic item that didn't fit into the cookie-cutter build design.
I didn't follow the exact progression of items season-by-season, so I'm not going to attempt to break them down 1 by 1, we're just going to fast forward to where we are today.
Season 7- Now we've got items that are combination of old ones that used to be separated so that you had to plan what type of role you were playing. Now you get the best of both worlds, but the results are far from balanced. The main demonstrative items are:
Mortal Reminder- Last whisper and Executioner's Calling USED to be separate items. You had to prioritize which kind of playstyle you wanted. You could deny an enemy healing, or you could go penetration to keep tanks from steamrolling you. NOW, you get both, which is a huge problem. Now you can not only deny enemies from healing, but you can significantly diminish their attempts to buy a defensive item to help their survivability. You have a dual-purpose item that gives far too much power.
Thornmail- This now gives health, attack slow, damage reflection, AND grievous wounds.... Why do you think that is? Because everything else is hitting WAY to f'king hard. It's a testament to how fk'ed damage output has gotten. Thornmail used to be a last-ditch effort type of item only used regularly by Rammus, Shen, and Mundo to deal with an over-fed ADC or Trynd. It used to be just 100 armor and damage reflection. Now it's gotta have 4 different properties just to keep up.
Phantom Dancer- I'm sure you remember the old big advantage of PD right? Yup, you got to ignore unit collision. What does it do now? It reduces the physical damage done to you by the last champion you AA'd by 12%!!!! TWELVE PERCENT... That was a privilege that only Urgot used to get, because he was so out-maneuvered by 99% of these new high-utility champions that he couldn't keep up. Why 12%? Because even the now hyper-damage ADC's are doing too much damage for their own good. Now we need to reduce the amount of damage the enemy is doing by killing it by 1/8th without ANY thought to buying defensive items. I'll go out on a limb and say that the only Melee AD champs that uses PD reliably is Trynd, so this is mostly an ADC item now.
Blade of the Ruined King- This one's just been a headache since its inception. %hp damage should NOT be available to everyone. Especially when you've got champs that ALREADY HAVE %hp damage built into their kits (Vayne, Kog). There's a reason they're hyper-carries. The active slow, active move speed steal, lifesteal, attack speed, and attack damage are enough. You don't need an item that has 6 attributes. That's too many, far too much power in 1 item.
Yes, these are mostly AD/ADC related items, but that's in response to the above mention of bot lanes carrying games too much. Okay, now take an ADC that has Mortal Reminder, PD, AND BotRK, you've now got an over-tuned killing machine that has the power to shutdown healers, tanks, mages, other ADC's, bruisers. There's enough attributes in those 3 items to account for 12 individual items. Now, half the time an ADC can 3-4 shot a mid mage or support champ if they've got the element of surprise or a half-decent peel.
It used to take skill to blow up an enemy champion. You had to have teamwork, and it took a hell of a lot longer than 1.2 seconds to delete someone. Now, these ADC's on steroids just walk up and 3 shot you. There's no fun in it. It's no longer a risk-reward type system, it's a "Whoever right-clicks and button mashes the fastest wins" system.
As for the new 'Rune System', this just amplifies the problem. Oh, the ADC is fed AF, has all these over-tuned items, and can already 3 shot half the team? Cool, let's give them a Rune that let's them shoot EVEN FASTER. Ya, fk it, let them attack 4 times a second, what could go wrong?
Why do the new 'Runes' have to give damaging effects? The old masteries were damn near perfect. Slightly underwhelming stat-wise, but they allowed you to choose your path and allowed you to play within it by shaping the ATTRIBUTES of your champion, not how much extra unnecessary bonus damage they do. The items now shape the attributes of your champions, and the "runes" just add extra damage to make up what new players and normies lack in skill. Oh, you landed a skillshot? Dude nice job! You're MOST LIKELY gonna miss the next one, so let's shoot a meteor at the enemy to add a little bit of extra damage in there just in case you DO suck. Oh, you can't plan ganks in advance and use the Ghost summoner spell properly? Let's give you a dope built-in boost with some extra on-hit damage so that just on the off-chance that you DO manage to pull off some half-assed gank attempt, you're probably still gonna do enough damage so as to not get disappointed or get your feelings hurt by your suckage.
You have to learn from your mistakes, not be rewarded by them. I learned the hard way. Either get good or get lost. If you can still wreck shit with half-assed and sloppy play, then the problem is not with you, it's with the platform. We need to smack baddies on the hand, not hold their hand.