This is not true at all. Plants are closing because of onerous NIMBY regulation. They can be made cheap if they are built at scale, see South Korea for an example of cheap plant production.
Indeed, SK produces nuclear so cheap that they are exporting plants to other countries.
Do you have any evidence for this? Can you point to any nuclear plant in the US (or anywhere else) that closed prematurely due to new regulations? I bet you can't.
As for South Korea... I'll just quote Wikipedia here.
"In 2012 South Korea had plans for significant expansion of its nuclear power industry, and to increase nuclear's share of generation to 60% by 2035.[2] Eleven more reactors were scheduled to come online in the period 2012 to 2021, adding 13.8 GWe in total.[3] However, in 2013 the government submitted a reduced draft plan to parliament for nuclear output of up to 29% of generation capacity by 2035, following several scandals related to falsification of safety documentation.[1] This new plan still involved increasing 2035 nuclear capacity by 7 GWe, to 43 GWe.[4] Responding to widespread public concerns after the Fukushima Daiichi nuclear disaster in Japan, the high earthquake risk in South Korea, and the nuclear scandals, the new government of President Moon Jae-in elected in 2017 decided to gradually phase out nuclear power. The three reactors currently under construction will be completed, but the government has decided these will be the last built, and as the existing plants close at a 40 years end-of-life they will be replaced with other modes of generation."
Indeed, SK produces nuclear so cheap that they are exporting plants to other countries.