Green hydrogen has to first prove itself that it can become economical viable. One of the biggest test trials for that is the Swedish initiative, and that one is mostly paid through subsidies and grants. Sadly it isn't looking very great even if the government did decide to continue sending more billions into the project.
Intermittent renewables and batteries will get us to 80% carbon free electricity generation for more quickly and cheaply than nuclear. While nuclear might make sense in the very narrow use case of 100% carbon free electricity generation, given we also need to decarbonise non-electrical emitters, it will probably reduce more carbon emissions per dollar spent to instead spend that money on even more cheap intermittent renewable generation capacity and use the excess to generate hydrogen. At the point hydrogen based fuels may make sense to use as a buffer for intermittent electricity generation.
But I don’t understand how the combination of nuclear, wind and solar would be low cost. Wouldn’t you effectively have to build out enough nuclear to cover still cloudy days at which point your wind and solar is not very useful? That sounds expensive.
I suspect we won’t end up building much nuclear because we will already have built out so much wind and solar. Nuclear is a poor fit for filling gaps in generation by intermittent renewables because fuel costs are negligible so it costs the same whether you run at 50% or 100% of rated output.
To eliminate carbon emissions entirely we will need some green hydrogen for turning into aviation fuel and as chemical feedstocks. Perhaps the gas backup will eventually burn that.