The title is mostly the question. Is it good to give everyone in the group the chance to be the GM, or should the best do the job always for best play experience?
The GM/Player roles are not symmetrical
In my experience, not everyone is suited, desires, or even likes to GM. The work required to show-up and play your character is almost always less than preparing to GM - reviewing rules [changes], creating worlds/encounters, prepping session materials, cross-checking player-submissions, etc. Even "lazy GMs" usually do more prep than their players - it is a side effect of the many-to-one nature of the game.
It's not for the timid. - so no one should be compelled to take on the role.
Finding out requires trying out
On the other hand, there are many folks who might be great GMs, if they only get the chance.
Earth Needs More GMs! Watching a great GM can be intimidating to prospective ones. Offering the rotation to everyone at the table is an excellent means to encourage trying the role on for size. And, as suggested by the question - allowing other game systems to be introduced as well can help with the fear of being compared to other GMs stigma.
"Hey! I don't know if I can do it justice, but I just read about this new system: XXX - and if you guys want, I'll try to run it for a one-shot next week..."
I think this is really up to each individual group. From what I have seen on this site some groups share GM load by campaign and other groups play different simultaneous campaigns with different GMs.
My group has kept to one consistent GM for our main campaign. However, myself and one other member of our group have started our own campaigns with the same group of people. We still play in our usual time and just give our regular GM time off to be a normal player.
This has the advantage of giving the main adventure the consistency of a single GM, but it also gives the GM a break and allows him to step into the player role. It also gives the players who want it the opportunity to get behind the screen and GM.
Our group has one primary DM who "owns" the campaign, but other people take turns as well running story arcs that are a part of the overall campaign. Basically, the primary plot belongs to our main DM, but from time to time, others of us have run arcs which belong to the same world, but which usually occur in other parts of the campaign world and only have a minor to moderate interaction or influence on the main campaign plotline. It's worked quite well for us. We've been playing the same campaign for nearly 15 years now.
When we do one-offs with other rules, such as an annual Call of Cthulhu session or two around Halloween and occasional runs with other rules systems then it's usually run by someone other than the primary DM.
I've been a DM for as long as I've been role playing. More often then not, I'm the DM for our games. The reasons vary from desire to creativity to just wanting to run the game. But it gets taxing and tiring and after a while, a DM will burn out. I'm not saying that the players should have to sit and take a break for a few weeks/months, but it helps a lot if you have different people to run games. This way, you don't get a DM to burn out or run out a material. I know I have more than once in the last 12 years. I think it's a very good idea, but note that it's not for everyone.
I've played in a longterm campaign with 1 DM, and another group where everyone DMs.
Benefits of many DMs:
Benefits of a single DM:
Disadvantages of Multiple DMs:
Disadvantages of Single DM:
In the final analysis, I think it comes down to a Coke/Pepsi kind of thing. I personally really like the many-DM approach my current group uses, but I do miss some of the long-term character development that single DM campaigns allow for. It is also somewhat frustrating when you've thought up some sort of wonderful campaign and are amped up about it, only to find it sit on a shelf for a year while you wait in line.
A gaming group is like a sports team. Like that team, you have a variety of concerns you need to balance.
Is everyone having fun/are we excelling?
If everyone's having fun, that's good. Sometimes GMs get burned out and don't want to GM, which means everyone's not having fun. Sometimes one or more of the GMs suck, in which case everyone's not having fun. Sometimes someone wants to GM but they are getting told "no, this other person is the GM," in which case they're not having fun. These factors vary from group to group and vary over time within the group, so you need to know how much people are enjoying the game(s) and their role(s). Talk about it.
But "are we having fun right this minute" isn't the only gauge...
Are we planning for the future; is our group healthy?
Having one GM, like just having one pitcher, can be a problem when that one GM leaves/graduates/has a falling out/burns out/gets married/etc. You want a deeper roster. So in many cases, you will want to let the person who's not your "best" GM do the job so that they get better. You will want to let valued members GM, even if they're not the best, because they are happy and will stay with the group if they get to GM once in a blue moon.
You have to plan for long term happiness, too.
GM Rotation Example
In my old gaming group in Memphis, TN, we had me as primary GM for years and one other guy who GMed some. When D&D 3e came out we all bought the books and I bought the first crop of 6 adventures that came out (mostly third party - hooray OGL!). I said, "I'll run the first one, but I'm as new to this game as anyone. I know some of you have GMed and some never have. But what do you all think about everyone taking a turn GMing in this initial round?" They all agreed and so inside the same campaign with the same characters, we rotated GMing from adventure to adventure. Some folks had never GMed; others had. The experience was extremely positive for everyone.
Once we had done that, we were very happy we had, and though some people went back to just being players, more chipped in to GM over time and even started side groups to run other campaigns; it helped turn the group into one gaming group into a network of related gaming groups. My group here in Austin is the same kind of way; nearly everyone GMs sometimes and as a result it's not one six person group, it's a group of maybe 4 or more loosely affiliated games. This provides a lot of flexibility in terms of player recruitment, game choice, etc.