It's not that we NEED locations... I just think it's a nicer idea then having gyms belong to types as it were. But then again, you raise a good point... the badges themselves tend to represent their element.
The only reason I suggest the possibility of a gym's type changing, is that there's a real possibility that someone who is a gym leader might want to quit, get bored of the whole shebang. In such a case, the next best non-leader player who wants to be a gym leader might not want to have a team of that type.
Then again, we could always just 'close down' the gym where the leader quit, and allow the 'opening' of a new one. Have gyms belong to their leaders, rather than leaders belonging to their gyms.
And again, good point on there now being enough from any given type.
Anyway, enough of responding, some new ideas for the pot:
Play gym battles by the anime rules - Leader decides on the number of Pokemon in a team. That way, if a certain leader wants to be like a game gym leader and only have say 2 to 4 Pokemon, they won't be at an epic disadvantage that the ingame gym leaders are (given that it would be very possible to have a team of 6 that all have a type advantage over any and all of the leader's pokemon).
Non-official gyms - If there are decent players deserving and wanting to be leaders but no gyms left to lead? A la Saffron Dojo etc. Might get too out of hand though, would need some selection process.
There's a problem with the possibility of a replaceable champion... Would you just switch out the old champion? Does that mean Gym leaders and E4 members can't battle to be champion? Or can they go on a quest getting the other 7 badges and beating the E4 / getting all badges and battling 3 of the E4, and then contend the championship? If so, would the ex-Champ have to take their gym/E4 place? Plausible. Better I think to disallow leaders/elites from contending the championship.
To summise that last confused paragraph, I think that the E4 and Gym leaders should be selected - by whatever process, voting, whatever. Then the first to collect all badges and beat the E4 becomes the first champion. Anyone who manages this chance after that may challenge the Champion, and if they win, they become champ. The ex-champ retains his or her badges, but must battle through the E4 again before fighting to regain their title. That's how I envisage it could work, anyway.
As for Leaders and Elites earning badges of their own, I don't see why not. In the anime the Leaders occasionally seem to be wearing their own badge, I think. And there's some mention of Brock being unable to travel and collect other badges...
And perhaps we could come up with some badge-like-thing to represent successfully beating an elite? If we're to make it quite like the challenges.
Just my two... four... six-ish cents.