All Honda mowers, fixed or adjustable throttle, have a governor device to regulate maximum speed; this to protect the engine from going too fast and potentially destroying the engine. The fixed throttle designs are usually found on mowers with the blade bolted directly to the crankshaft, and a flywheel brake is used to quickly stop the engine (and blades) when the controls are released. Adjustable throttle models (with an actual throttle lever) are usually only found on mowers with a blade-brake clutch (a.k.a. "Roto-Stop") as this allows the operator to release the control lever, the blades stop, the engine continues to run. They can then use the throttle control to manually slow down the engine before the remove the grass bag to empty, or to walk around and remove a branch, Frisbee, etc. out of the mower's path.
The same basic design of the governor and its parts has been unchanged on Honda OHV GX-series engines for nearly 30 years. The more "modern" GCV engines (introduced in the mid 1990s) use nearly an identcal set-up, but also feature an internal timing belt and more shared parts between the horizontal and vertical shaft models. All but one of Honda's current mower line-up uses a GCV engine and properly maintained, it will lst for many, many operating hours and years of service. Governor failure is very rare. 99% of the governor issues I've seen are when they are disassembled and not put back together properly.