I don't think the system actually works the way you are implying it does. The question is also a bit broad (why do i play against / get the teams i get?).
First there are different MMR's depending on what queue you are in. If you are in a normals queue, you will have a different mmr than if you are in a ranked queue. This also is different if you are playing summoners rift, twisted treeline, or other modes.
For example, I have a friend who is gold 5 in solo queue. He used to main twisted treeline however. When he plays on summoners rift on normals he generally plays with silver / gold. When he plays on twisted treeline it is not uncommon for him to play against diamonds, masters, and challengers. This is because you don't have just one mmr.
This is important because based on what queue you are in you not only have different mmr's, but those queue's will have different priorities. Ranked games put a priority on trying to have very even teams in terms of mmr. While normals want to have even games, but also don't want players to wait too long to get into the game. So in normal games you are more likely to get a wider spread of mmr's and have more unbalanced teams.
This also changes based on when you are playing. If you play during 'peak / high traffic' times then it will be easier to find other players around your skill level to play with. If you are playing when not many other players are online, you are more likely to get a diverse range of skill levels to play with (especially in normals).
This is why ranked queue times generally are longer than normal queue times. They have different priorities and ranked queue's place a high priority on competition and trying to find even teams.
Also, I have never seen teams so diverse (I know you are exaggerating as well) as the ones you listed in a ranked game. The only times i've seen teams with huge skill gaps are in normals and this is usually due to pre-made teammates. So those four bronze players may be playing at 3 a.m. when not many people are on and are all queued together. Even then this is unlikely but can happen.
An example : I was playing at night (about 3 or 4 am) a while back. I was playing a normal solo, and everyone on my team was around mid plat. The team we played? 4 diamond 1's and a challenger. They were queued together. We didn't play them because we had similar normals mmr (no way), we played them because not many people were playing at that time of night and the system was having trouble finding another team of players, queued together, with challenger-ish combined mmr. Result? They probably waited a while in queue and the "fair game" definition got expanded to include our team of mid plats.
I also doubt that the system takes 5 random people, adds there mmr (or combines it), then tries to find another randomly made team. This would be so annoying and not very efficient. They more likely have pools of players who when entering queue get put into different mmr pools/buckets. The system then tries to find 10 (or very close to) in the same bucket and place them on teams in a match. If it can't, the system either has to wait for another drop (player) to enter the bucket, or get a bigger bucket (expanding the allowable player pool). The first method takes longer (ranked priority) the second option has a larger variety of mmr's (normals priority). I also think that both of these options (and possibly more) are used during matchmaking.
One last bit, this is also just put together from what I've (and other people) noticed. Only Riot really knows how they do their exact matchmaking.
Hopefully this makes sense, if it doesn't somewhere just let me know and I can clarify!
