In the summer Olympics, Idon't think you'd be able to run Evetning all with the same horse so you make a good point overall. However in sailing, they do run the same boats, same gear though the crew (or sailor) can adjust per his/her style. In this case then they do take teh equipment out of the equation.
The problem I see with toiday's Games is that money is the driving factor. I know, an obvious statement, but still one to be made. THos with the money get the best equipment. Got $100,000 then you get the better horse then another with maybe more talent, but less lucure. Better high tech boards, bob-sledes designed by NASCAR engineers help to skew the competition.
In sports where equipment is not the main part of the action (suits for example) then everyone where the same outfit. In sports where equipment is a factor, there is a moment when teams/players have to switch equipment and play again. Jamacia gets to ride with the US sled, the US with Irans. The better team will over come equipment issues. Even with Eventing this could happen though I'd lower the jumps a little to save lives.
Back when the Olympics was about amatuer athletes was when it was worth watching. Now it just is an extension of continuiong world sport events where I watch the same professional compete agaisnt each other....boring. There is not sotry in Bodie Miller any more, Shawn White is not who I want to see in an interview. Even my own sport Eventing has been corrupted to the point where I don't care to watch it. Given the amount of corruption embedded into the Olympic machine, why do we want to support it any more.