Extracting uranium from seawater on the scale needed to fuel burner reactors requires massive engineering. The estimate I've seen is that fueling one 1 GWe burner reactor takes a seafloor uranium absorption field (suspended in a strong ocean current; if you have to pump the seawater yourself it's already too expensive) of 170 square kilometers. The power/area is already much lower than the time-averaged output from PV.
Extrapolating from the lab bench to 170 sq. kilometers (x 6000 for the number of reactors needed to power a nuclear world) is a far larger stretch than extrapolating renewables and storage to what they would need. Your selective doubt is not being driven by any honest impulse.