Even if you look U-235 alone, we have at least a couple centuries of it using conventional reactor tech, based on the known (explored) deposits, and very conservative estimates of how many more we will discover once existing stock starts to dwindle and prices start going up. Less conservative estimates give it closer to 5-6 centuries.

Now, if we use the tech to its fullest extent - meaning U-238 breeder reactors, rather than conventional U-235 ones - then fuel supply is infinite for all practical purposes. It also by and large solves the nuclear waste problem.

The main problem with nuclear isn't price per watt, it's the upfront cost. It requires a massive initial investment before you start getting anything useful out of it, and it requires an even more massive investment to start deriving benefits from scaling up. Solar, on the other hand, can start with a very small investment, and gradually ramp up, with a smooth curve of decreasing cost as scale increases. That makes it more attractive to private sector.

Nuclear is something that pretty much requires very long term planning and subsidies of the kind that only governments are really capable of, and in the era of democratic governments and nuclear scare among the general public, it's just not happening.

Well, except for countries that don't have to care about public opinion. China, for example, is building a lot of new nuclear plants. They aren't ignoring solar, either, and they're making massive investments there as well - but they're not putting all their eggs in one basket.