I can sympathize with your plight. I too get frustrated that players don't understand how to back off after they gave over kills to their laner. They come back and play the lane like nothing happened and then get killed again. Especially bot lane with double kills. That snowballs them harder.
For some reason players only have one speed, "go". Just keep hard pushing their lanes. They can't stop themselves from attacking the waves and trying to trade, and guess what. They are overextended and die to a gank or an all-in with an item disadvantage. Learning how to stabilize a lane after you give a kill is important. Its how you stop the snowball. I am not above this as I am S3. Usually after I die to the gank in that scenario, I get really mad at myself because I know better.
As others have stated there isn't much you can do. The match making does put you with others that are your MMR. The problem is that the placement system is fucked up. All new Ranked accounts usually get dropped into Silver. So it can feel like you go from playing with others that have your awareness and game knowledge to players that aren't any better than bots.
I personally feel that all new ranked accounts need to be placed into a separate unranked tier with only one division. They are required to climb to 100 LP and win a bo3 promo. Once they do that they are placed in Bronze. Here is my reasoning. This will/should do the following. First, Bronze will actually be a goal to attain instead of being crapped on (even though it is the bottom tier, at least you have to climb to get to it). Second, it will stabilize Silver as it is noted to have the widest gap in skill of all the ranked tiers and has the highest population of players. I feel this will help smooth out the tier.
If the new account is unable to climb out of the unranked tier then there is a reason and they will need to improve to do so. Once you climb out of unranked you will have the placement matches for any new seasons like we have now.
I have played with people in silver that are just slowly demoting out but the system intentionally tries to help them climb so it takes them forever to fall. While this is happening they are negatively affecting the games of players that are actually climbing. This has created a negative experience for me and a large amount of frustration. I understand that I am going to lose games, I just don't want to lose because the player is in the wrong rank. Riots system of auto placing new accounts in Silver is pretty bad.
The first time I did placements I was put into Silver 4. I demoted to silver 5 and stopped playing because I wanted a silver border for my year end reward. This was 3 years ago. I recognized at the time that I was over my head. The next year I was placed B4 and I slowly climbed to Silver 5. Last year I started Bronze 3 and ended Silver 3. I maxed out at Silver 2 100 LP before I went on a losing streak that I blame on matchmaking. it was unreal the bad players that I got on my teams repeatedly. I demoted back down to Silver 3. I stopped playing ranked 2 weeks before the end of the season because I was so tilted. This year I started Bronze 2 and am currently silver 3. I recognize that I am still pretty bad at this game but my point is that I should not have been placed in silver my first year.
This whole long reply post is to show that I really do understand what you are describing. I hope the new ranked system that riot is going to deploy next year will address this issue. new accounts in silver creates an unneeded impediment to improving and climbing the ranked ladder.