Currently nuclear reactors take well over a decade from construction to start of operation. I think few are willing to bet that storage will still be a problem 10 years from now.
Carbon capture from gas natural gas (also an alternative that exists today) is another technology you’d have to bet won’t become economically feasible by the time your nuclear power plant finally becomes operational.
Honestly a base-load alternative is not such a strong argument in favor.
I’m looking at the list of reactors on Wikipedia and what I’m seeing is pretty much a 8-10 year minimum from construction start to operation start. China is a big exception to this patterns (taking 7-9 years), but China is in a league of its own when it comes to mega-projects. The of the few reactors that did start operation outside of China in the past 20 years there is often some involvement of Chinese construction. (e.g. reactors 2 and 3 in the Karichi nuclear plant). In Europe, Rostov is one of few that seems to have broken the 10 year minimum with their 3rd and 4th reactors (7 and 8 years respectively). But reactors 1 and 2 in the same facility started construction in 1983 but didn’t start operation until 2001 and 2010 respectively.
Scanning the list of new reactors it seems that 8-10 years is a reasonable estimate for reactors in an existing plants, and close to 20 years is a reasonable estimate for reactors in new facilities. This gives 2030 as the earliest reasonable time for a new reactor in an existing plant outside of China that you already have the design for, and 2040 for new facilities if you are starting your planning phase now.
Are you willing to risk that energy storage is still gonna be lacking in 2030-2040? Are you sure carbon capturing of natural gas plants will still be economically unfeasible then?
Honestly though, if we still haven’t sorted out our carbon emission before 2040 I think we have bigger things to worry about then 24 hour access to energy at a low price.