The cost is a choice. Not inherent to the power. We could choose literally any day to make it dramatically cheaper.
PV solar + batteries is a dead simple, solid state design that's easily scalable without huge up front capital requirements. We're not at the point yet where nuclear doesn't pencil out anywhere, but with current trends it's getting closer by the year.
I wish we built more nuclear 20-30 years ago when the competition was coal and gas but unfortunately we didn't and now the equation has changed. Shutting down existing reactors that are still viable is a bad move to be clear, but new plants are becoming increasingly hard to justify economically.
That's a very ambitious statement, every piece of hardware has lifecycle limitations. Engineering things for "infinite" lifetime significantly drives up the cost of the resulting product in most cases.
I would certainly hope the radiation-exposed parts of nuclear power plants are engineered for a very long life, but… there's water and metal involved, these things do need maintenance. And the non-irradiated parts probably need to be maintained much more frequently, e.g. the turbines certainly won't live forever.
As a matter of fact, solid state devices tend to last much longer, and PV is one of very few completely solid state power generation technologies. (It does, unfortunately, suffer from general sun exposure damage.) Personally speaking, without some digging I wouldn't make any claims which of them lives longer, it feels like it could go either way by quite a bit of margin.
I would love it if somebody who has recently built something like a fission plant could give us a report as to exactly what happened that caused this.