Carbon emission has an almost direct relationship to the amount of fuel burned, so assuming single occupancy, even older motorcycles do fair better than most cars in that respect. Particulate and NOX emission, not so much.

It's mostly for bikes before Euro4/5. Obviously, new bikes are one thing but most bikes in the USA are offenders of pollution.

A statistic for CA was motorcycles make up 1% of my miles driven but 10% of smog pollutants.

Bikes didn't require catalysts for a long time. And they often used less-precise fueling systems, like carburetors. But that has changed or is changing in a lot of places more recently.