Here is why you cant solo carry, and why the game feels awful.
Is it because of this high damage meta? or the unbalanced champions in the game? getting instagibed by everyone?
Damage was always here, its here now, and it has been here when assassins were meta, remember when you would get deleted by katarina, fizz leblanc, rengar... yet the game was fun. Unbalanced champions? they were always here as well, you would have champions who got OP broken at times, and those who were left OP for ages without being nerfed, (i'm not going to throw names to avoid tangential replies.)
Yes giving high damage to any champions despite of their role is a problem, as demonstrated by support mages in the bot lane having kill potential thanks to aery/orb/electrocute damage, which shouldn't be there, but that's beside the point. You want to know why the game feels awful right now? its mainly because of two things that go back to back.
WEAK TURRETS and POWER CREEP
why is that such a bad thing? why cant you snowball anymore because of that? why can this successfully prevent you from climbing?
Before these changes took effect, if you were really good, you could snowball the game and possibly win 1v9, you just have to get fed right? you get fed by killing your opponents, and you accumulate kills to the point where you are unstoppable, the other fed opponents cant face you, you are so fed too and you are a more skilled player, you have every chance to outplay them, and your good decision making of when to roam and making good calls cannot be matched by them, you can solo win the game. key word you are REALLY FED which takes TIME.
Now lets see why you cant do that, lets assume you are playing top or mid or bot, lets leave jungle out of it, since there are too many variables to take into account, you killed your opponent once, twice, great i will carry this game! "your team's turret has been destroyed", three kills ! "your team's turret has been destroyed", if you roam and God forbid you take too long, "your team's turret has been destroyed" ( yours )
Now you are forced to depush/help the bot/mid/top lane because if you ignore it you will probably lose the inhibitor at 10 mins but wait? if you do that you will lose your mid/top/bot turret? so how exactly are you supposed to solo win? if the losing lanes cant even push the said lane opponents from piercing their way to the nexus and getting fed in the process? which can happens before the 10 mins mark, you simply cant get to the point of 1v9 when the turrets are too weak? and guess what thanks to the POWER CREEP that lane is gonna push like crazy, now you're stuck there while the enemy team is getting objectives and closing the game in.
Better yet, how is this going to prevent your climbing? simple, very simple, even if you have the potential to get 4 bad players vs 5 bad players on the enemy team, your opponent doesnt have to win, in fact he just has to play like an absolute chicken push the wave and hug his turret and you are f****, while if any of your teammates feeds he will get pushed to the inhibitor by the 15mins mark. depending on the champions of course.
Answering some potential questions :
If your opponent plays safe why not roam? Because the turrets are so weak one roam might cost you a turret, and if the opponent has any decent waveclear / turret damage its out of the question.
Why not push keep pushing after you kill your opponent? what if your champion inst very good at pushing quickly? when you pick a champ that can 1v5 its not guaranteed that they will have wave clear / strong turret damage? or what if the jungler comes every time to defend their lane? ( happens a lot mid ), or what if they play safe? then you might not be able to force kill them.
Grind your opponents turret / freeze and deny him farm / dive him? what if you are melee? or your opponent possesses hard cc so that you ca neither dive him nor grind his turrets hp? and deny him farm? whats that going to do, you don't have time for that the other lanes turrets are falling one after another.
all in all, the game should be like this : you chill, farm, wait for mistakes, punish your opponent smartly, that's how it used to be. now its try to get fed as fast as possible, force trades, make mistakes and get frustrated, because of that ticking bomb placed on turrets.