In a recent study, researchers from the European Environmental Bureau (EEB), the Stockholm School of Economics (SSE), and the Potsdam Institute for Climate Impact Research (PIK) questioned the planned development of new nuclear capacities in the energy strategies of the United States and certain European countries.
You’re right, and that’s why it would be foolish to build exclusively nuclear. It’s also foolish however to not build any nuclear. The long lead time means we need to start ASAP so it’s ready ASAP. With proper government action targeting bottlenecks in the process (I believe there’s only one manufacturer in the world for a certain type of reactor shielding) we can speed that up.
Diversification is the way to go. At the very least, we should build enough reactors and breeder reactors to consume existing nuclear waste and drive that to effectively 0.
On top of all that, the bottleneck for deploying solar and wind en masse isn’t actually solar and wind facilities (although we certainly need those) but our electric grid. It needs an upgrade in order to integrate alternative energies, and I believe estimates on doing that are ~10 years. We might end up in a situation where a nuclear reactor is actually faster to build, depending on the type.