Flex is totally different from solo/duo and the problems with flex are very much different than in solo/duo. In flex, you can queue with your silver friends even if your diamond since your flex rank is the same as your friends which completely screws the MMR balancing of the game. I've had games in flex where the MMR differential is 400 because of this which makes flex fairly uneven.
The problems with solo/duo are different because you can't queue a diamond player with bronze player (unless smurfing/duo boosting). So what are the problems with solo/duo? From the perspective of the boards, it is Rito working against them by matching them with trolls, feeders, etc on their team causing a sudden streak of losses after a couple of wins. Additionally, as OP brings up, "Why is it that in my promos, the teams will be equal, Plat 3s-Plat 1s Vs. Plat 3s-Diamond 5s, but yet, when I get promoted I get a Gold 2/3 on my team and some Plat 4s to carry against a team of Plat 3s and 2s?"
The answer is simple. MMR Matchmaking. For the same reason you will get "uneven" teams at rank face value (e.g. a gold with plat mmr vs a diamond with plat mmr due to the gold going on a win streak and diamond on a loss streak) you will be able to climb as the gold in this scenario "Why have the league system if you are going to just face people of your own skill anyway? How will a person climb from Gold 3 to Plat 5 if they are constantly matched with people that are Plat 4/5/G1?"
Let me elaborate. If the Gold 3 is going against G1s-P4s then it is probably due to the Golds MMR being equal to that of the G1s-P4s. When your MMR is higher than your current rank mmr you gain more LP than you lose. So if you're up against equally skilled players (e.g. your level MMR players) you will continue to climb EVEN IF WIN AS MANY GAMES YOU LOSE. When you are winning as much as you lose then you are at that level of skill. Losses are expected after large win streaks you will start to be matched against equally skilled playersso you will start to win 50% of the time.
Let's go back to the Gold 3 example. The Gold has been winning a number of games because he has been matched against lower skilled players and therefore his MMR has increased to a Plat level. He will start facing against Plats equal to his and although he wins 4 games and loses 4 games he still gains a net +40 LP since he gets +25 LP on a win and -15 LP on a loss. Yet he only gains 40 LP when he needs more than 200 LP just to get to G1. Why is Rito making this harder for him???? And what about his promos? If he wins as much as he loses than it's likely that he will win a game to get into his promos, win another, than lose the next two losing his promos!!!
Here's the thing. Rito has added the MMR system to make it easier to climb. If you're MMR is high enough, you will skip divisions. In the case of the Gold 3 I do think it's possible but I think the alternative that he will be placed against Gold 2s and 3s lower than his skill level yet equal to rank is much more likely. I say this from personal experience. When I recently climbed from Gold 3 to Plat 5, only occasionally did I get a game a against equal MMR players. For the most part, I was facing against the same rank players making it much easier to climb. I only started frequently facing against Plat 4s when I was G1, at that point where the ranked discrepancy is not that high (compared to Gold 3 of course).
Rito has overall made the ranked system a much better place to climb due to MMR. It's easier since you gain more LP than you lose if your hidden mmr is higher than your rank mmr, get a free win on your second promos, can skip divisions., etc. It's also much easier to spot where your "peak" is. Example if you went on a long win streak and climbed from Silver 2 to Plat 4 but suddenly lose a few than you can assume that you're probably around the Plat 5 level.
It also should be noted that if you get trolls, feeders, etc on your team after a win streak it's just UNLUCKY and no more. You never hear about the people who got a free promos due to an afk twice on the enemy team. My Plat 5 promos was so free because of this. I played two games in which the enemy had a troll and got easy wins. I've also had games where the opposite has happens and I get the troll. At the end of the day, it's just unlucky and knowing whether or not a player will troll in a ranked game is out of control of the match making system.
Any questions?
TL;DR
MMR system helps with climbing. You can climb with a 50% winrate with the MMR system since you gain more Lp than you lose with high mmr. Just unlucky with trolls on your team.