Can a motorcycle be ridden without an exhaust pipe?

The main reason a motorcycle cannot be ridden without an exhaust pipe is that the exhaust pipe is part of the engine's exhaust system, designed to eliminate the exhaust gases produced during combustion. Without an exhaust pipe, the gases would be released directly into the air, which is not only harmful to the environment due to polluting emissions, but can also negatively affect engine performance.
The exception for electric motorcycles is because they do not generate exhaust emissions and therefore do not need a traditional exhaust system.