The factory design for virtually all MTD Model 137-504 Transmatic ride-on mowers included an engine cover, If you're looking at one without a cover, it's almost certain that the original cover was lost or removed.
The covers had a few functions.
For models with the engine in the rear, the enclosure was particularly important for safety, as it protected the operator from the hot engine and moving parts.( By fully enclosing the engine, )
Engine Protection: It offers superior protection to the engine from all sides, shielding it from debris, branches, and other hazards.
Noise Reduction: A metal box enclosure would significantly help in dampening the noise from the engine.
I can't find a good image online but from memory I thought they had a plastic cover on top of the motor.
The Problem with Old Plastic: Over time, exposure to sunlight (UV rays) and extreme temperature changes (from a hot engine to a cold environment) causes plastic to become brittle and weak. A minor impact that wouldn't have damaged the cover when new could easily cause it to crack or shatter on an older machine.
There are a few manuals online for this mower if you use Google.
