There was a controversy in curling a few years ago where some curling teams were using new brooms by a new company that had significantly better tech. It was so good it made it unnecessary to have two sweepers. The resolution was to ban it and only allow brooms from certain manufacturers.
It seems reasonable that these sports could narrow down the list of approved equipment down to a few approved suppliers every year.
Shoes had a similar issue when Nike released their first modern super-shoe (Vaporfly, IIRC). The track and field body had to limit shoe sole height and the other brands had a lot of catch-up to do.
Same for swimming with high tech, low drag, bouyant swimsuits. Again, the international body had to step in and ban some materials/designs to prevent domination by nations that could sink resources into the engineering.
same thing happens in cycling all the time too. the UCI bans new equipment all the time, and the rules for what is allowed are very strict, to the point where there's a limit on sock height. there is a limited list of frames that can be used in UCI races, including the olympics
but rules around the type of equipment you can use, and the race host supplying specific equipment to all riders, is a very different thing.
Did you know that the Olympics used to be a strictly amateur competition? You would get disqualified if it turned out you'd taken payment for your sporting activity.
The idea is that different equipment is better suited for different individuals. By mandating a specific kind of equipment for all athletes, you'd be benefiting some individuals over others.
For example, road bikes have different frame shapes that are suitable depending on your torso length compared to leg length.
Of course, the natural next step would be allow some flexibility (different frame size but same material), but you can see how that could be a slippery slope of legislation and lobbying that would end up in a similar situation to where we are today?
You -should- be able to just mandate Hubs and cranks to get around this.
Or make sponsors provide a 'slew' of wheels and cranksets for all their riders (i.e. spares as well) that can get inspected before the race, and are randomly distributed between the riders sponsored.
Buuuuut UCI hasn't even figured out doping, so lol
Suggesting everyone should have to use a specific bike is exactly a suggestion like that - bikes have sizes and shapes that are suited to riders of particular body sizes and shapes.
Especially in the context of the original olympics, which were largely conducted nude. The idea that a rich country can field better equipment is absurd.
Would you expand that to nutrition, training regime, traing location (altitude), etc?
Then limit the amount each country/athlete can spend, make everyone get paid the same by different sponsors?
I don't think the Olympics were ever about equal footing or decreasing variables. To really level the playing field you'd have to have a clone army of athletes with the same genes, diet, lifestyle, training, coach, sleep, etc. Equipment is just one variable among dozens, and eventually the rules can change to limit their contribution (like with swimsuits).