To be sustainable, nuclear also needs to be sustainable economically. There's a cost problem with nuclear that often gets swept under the carpet by its proponents. But it's actually a big reason for its current lack of popularity.
Nuclear proponents instead love to emphasize how safe nuclear can be and how great of a safety track record it has. And with some caveats (e.g. the Fukushima mess was pretty bad) they are not wrong for modern nuclear reactor designs. However, nuclear is expensive and that combined with safety (which costs money to mitigate) is the real reason for the impopularity.
It always was expensive but historically, a lot of that was paid for out of tax payer money. Most new plants are still very expensive compared to almost everything else in the market. And they still involve a lot of taxpayer money.
Nuclear is not economically sustainable currently and those cost are either not payed (many countries don't have permanent waste storage solutions) or basically payed for out of tax money instead of revenue. If you add it all up it makes an already bad cost picture worse. Even without that accounted for it is easily the most expensive form of power. With all that accounted for, it only gets worse.
To be economically sustainable, it needs to become vastly cheaper and account for the full cost.
Will it always be that expensive? There are definitely ways to lower cost and there is of course a learning effect. But it seems we have a lot to learn. About an order of magnitude's worth of cost. And that would just be catching up to the status quo.