Unless there's a spiffy explanation somewhere, I don't think you're missing anything. You are correct that fission power plants create heat, which boils water in a steam generator to well, generate steam. That steam drives a multi-stage turbine, which drives the main generator to create electricity. The reactor and its support systems on the primary side, the steam generators, and the secondary side systems leading to the turbine generator are huge. And the efficiency is only around 33%. A big part of the limitation is the use of water for transporting energy. There's a term called enthalpy, which is a measure of the energy in a material. Water reaches its peak enthalpy at around 900°F. In order to bump the efficiency, to get more power out, ideally, you'd want to heat your working fluid more, but with water, that doesn't actually get you anything because of the enthalpy. So, to get more power, you need to make the whole thing bigger. That works for something like a ship, but not so well for a battlemech. Now, 1000 years of engineering and some handwaving can go a long way to making it more feasible. Using an exotic working fluid instead of water, that can be heated well beyond 900°F to it's maximum enthalpy, and you're most of the way there.
Don't get me started on shielding the mechwarrior from the radiation...