Correct. The base chassis of an Omni doesn't move any faster than the fully loaded versions, either.
Think of it as not just the engine that has to be able to deliver the output, but also the myomers and actuators must be able to perform the faster movement, which they simply can't, and all other moving parts must be able to withstand the increased stress coming with faster movement, which they don't.
The actual out-of-universe reason is purely balancing, though. Otherwise people could create underweight 'Mechs and just claiming that they now move faster. To prevent things like that, the rules are as strict as they are.