You're correct. The design of nuclear reactors was intended from the beginning to replace steam generation, with the goal of not needed to redesign the entire generating plant and take advantage of the known tech as much as was reasonable. There were ideas around for just replacing existing coal/gas/whatever with reactors, to get the most value out of the capital expended on the plant. There are still studies around retrofitting retired coal generation with nuclear reactors.
Just like steam tractors were designed to replace horses.
Which is a fascinating factoid really, because the farm tooling was designed to run at a certain speed (maybe not intentionally, but, over time, that's the design criteria regardless), so the tractors were designed to run about as fast as a horse so all existing tooling could be retained.
It wasn't until much later that tooling was redesigned to work faster.
