100% correct. Not only have nuclear costs not improved in the three quarters of a century it has existed, it's only gotten more expensive while wind and solar have plunged, dramatically, in costs.
In the US, nuclear capacity is being replaced by wind and solar at six times the rate it's being "lost"; the hysterics you read here on HN and reddit are just that. And the rate of solar and wind deployment is skyrocketing. The people building grids and investing in generation are putting their money into wind and solar, because it's the cheapest and easiest.
"Several years" is an understatement; it takes years just to go from "everything is completely constructed and wired and plumbed" to "we are connected to the grid." This happened in Canada, where a reactor at an existing plant was brought back into use. The process took years.
You can't just drop a nuke anywhere. In order to be cost-effective, they have to be enormous and run at full capacity as continuously as possible. You can't just drop gigawatts of power generation anywhere you want in the grid,so the grid might have to get reworked or a plant might only be feasible in a handful of geographic locations. The plant needs access to massive quantities of cooling water, and a geologically stable area. They also need to be able to suck down enormous amounts of power, because even when a reactor is shut down and not "generating power", it requires many megawatts of electricity to run all the cooling systems; a reactor takes weeks to stop generating significant amounts of heat. Ditto for startup (this is true of many plants, but especially nuclear.)
They take many hours to adjust power levels. That's not what the grid needs; the grid needs highly reactive power, on the scale of seconds to minutes. Pumped hydro has been doing that in the UK for decades, helping the national grid meet the famous grid surge where everyone flips on their electric kettles when the BBC goes to break during a programming. The pumped hydro facilities in the UK and EU can react within seconds to changing grid demand. The US has pumped hydro as well, but battery systems are getting so cheap, they're competitive and don't have the risks hydro dams do.
Reactor vessels aren't built on-site. The majority are built by Japan Steel Works, one of the few companies in the world that makes reactor vessels. They have fixed capacity, require very high grade metal, and so on. One cannot just snap fingers, throw money at the problem under a "green" funding bill, and get more reactors.
There's also the massive carbon footprint of construction and commissioning, which takes another decade of operation to break even on, if nuclear reactors ever break even. The industry almost completely ignores the carbon impact of mining and refining uranium as well as the carbon footprint of the massive supply chain and workforce it takes to keep a plant running. Meanwhile, solar and wind pay back their carbon footprint in a matter of months to a year or two at most.
We need the very fastest ways to reduce carbon generation, and that will only come from conservation, a radical shift in transportation policy (namely discontinuing subsidizing low occupancy vehicle use), and large-scale conversion to electricity as an energy source.