A better explanation is that Balance of Terror was an early episode, and they still hadn't fleshed out what exactly impulse power was yet.
That's no fun.
I'm going to have to watch the Horizon episode of Enterprise and see if they explain anything about their power systems.
I see it as most races develop impulse drive and choose the same power source for it as they develop one that allows impulse to be used efficiently. As a result that power source becomes "culturally linked" to Impulse drive and gets referred to as "Impulse Power" and "Impulse Engines". The same then happens when Warp is developed.
Impulse drive and Warp drive may under this thinking be powered by a variety of systems but not at an ideal efficiency. A Warp drive powered by a typical Impulse engine might cruise at Warp 2 (freighters). With an optimized Impulse engine perhaps warp 3. Given Matter Antimatter for Warp Engines Warp 5 becomes possible. Add Dilithium and warp 9 is achievable.