Yes, sailing. I believe all but Formula Kite are one-design classes (Laser, Laser Radial, IQFoil, Nacra 17, 49er, and 470). A few have options between licensed manufacturer (but to same spec) and a few are true one-make (Laser, Laser Radial), not sure about the others.
Single-design classes are standard in sailing, so the olympics uses them also. They are not standard for cycling, and it would be a huge deviation from conventions of competitive cycling for the olympics to demand them.
That doesn't mean they can't or that it wouldn't possibly be worth while. But there are huge costs to doing that, like possibly few or none of the major competitive cyclists competing.
I’d love to see track cycling get more standard equipment. As it is today, some nations pump a ton of money into aerodynamics and RR to substantial advantage. More so than the difference between a Cannondale or Specialized road bike. Or so it seems to me.
The Olympics (or, perhaps more generally, national team cycling events) _do_ make a huge deviation from the conventions of competitive cycling already: no team radios. One of the reasons they are so fun to watch :-)
Another exception is that the Olympics and world and continental championships are ridden with national teams instead of the various commercial teams. That makes quite a difference too.