eroginous, you seem to have little idea at all about how the system works. To give you some idea read
http://en.wikipedia.org/wiki/Elo_rating_system
The way the system is setup is that everyone should be winning about 50% of their games assuming they are playing against teams at their skill level. Now because there is no way to see how good a new team is they are given a buffer of about 100-200games to find the rating their skill level is. This buffer is the difference between your MMR and your team rating. When those are about equal you are at your correct rating. The reason said buffer is needed is so that you and your opponent isn't overly penalized or rewarded for playing against someone that might be much better or worse then them but haven't reached their correct rating. So until the team rating and the MMR about the same, you should consider the MMR your real rating and it takes 10-20 games to have that relatively correct.
To take your example of your own team and the 1867 rated teams. Your team has won 55% of your games and has relatively low number of games played so you are still climbing and you most likely haven't reached your real rating.
The other team has allot of games played and have relatively close to 50/50 win/loss ratio. This means that they are at their real rating, getting the occasional boost because they are either getting better, get lucky or play more against overrated players then underrated players. Also there are some inflation problems in the arena system that will increase their rating slowly if they continue to play.
As I understood it you only played 1game against them. The reason you won against them can be one of many like your actual rating should be about the same as theirs, they played badly, you got lucky or you have team setup that counters theirs well.
Elo systems have problems and there are different elo systems that reduce some problems while increasing others. The Arena system seems to have a relatively high inflation, mostly because there are way more games played by an active arena team then most other places where elo systems are used.
Your suggested system is similar to an Elo system but it has very high inflation and none of the safe guards real elo systems have against abuse and inflation. In a real Elo system if 2 teams are equally rated the team that won will get as many points as the loosing team looses, further if there is a 200point rating difference the lower rated opponent should win 1 of 4 matches so if 2 teams with 200point difference played 4 matches where the lower rated team won 1 match both teams should have the same rating as before the games(this isn't completely true over a small sample size because the ratings change after each game).
Now if we change your system so that for every game teams lost or won 10 points for absolutely all games this would result in basically the same system as is currently in play except you are penalized for meeting someone higher rated then you and rewarded for meeting someone lower rated then you and it would increase the queue time seeing as there might not always be teams with in 50rating of each other though reducing it from 200 would of course lessen the biggest flaw in your system. And seeing as your suggestion was meant to make it so that you couldn't just grind your way up with 51% win/loss ratio, you would still go up 20points for every 100games you played.
If you would have had it 10/-3 like you suggested, 70% of the teams would reach 2350 sooner or later. because you start at 1500 a team that drops below 1400 would just start a new team further increasing the inflation. Lastly no one would play more then 10games to get points if they are above 2300 or maybe they would just play enough games to both get points and get to 2350 again. Getting to 2350 again wouldn't be hard seeing as they would only need to win 1 in every 4 matches.
MMR didn't exist in the first seasons of arena and was introduced to fix the problems your system has. Lastly your system has a major flaw in the fact that there is no bell curve to your ranking making it inevitable for teams to reach the top rating and being equal at the top. The point of a ladder is to rank the teams based on skill and not reward loot. Now I am not a big fan of the introduction of rating requirements for loot seeing as loot complements your skill level. But it isn't so bad seeing as far as you will never meet a player with more then 4-5 pieces more then you if you are at your correct rating and you have all the gear available to you. Such a gear diffrence can be the diffrence in a tight game but it seldom is at the lower levels.
The biggest problem with the current system is how many new teams are made. I think there should be penalties for changing a team, like a maximum number of teams a character can play for in a single season( maybe 3 ) and you can't join a new team for 2 weeks if you leave a team. New season should remove all penalties and no penalties should be given the first week of a arena season.
Lastly to those saying he is wrong about the rating of an average player should check some battlegroups and see what the median team( team ranked in the middle of all teams ) has in rating. In most cases it is about 1300. Now because there are always allot of new teams the average rating is in reality higher then 1300 but I doubt it is over 1500 and the system is created to have the average player at 1500. Just think about your average PuG battleground group and then consider how those players are in arena and you will soon realize that most players are ranked below 1700.