Simple cycle gas turbines are 20 times cheaper than nuclear power plants of equal power output. So, no, your argument doesn't hold up when the actual numbers are examined.
Being 20 times cheaper while producing 2% of the kWh because they're turned off 98% of the time makes them 250% more expensive per kWh. And that's comparing the the capital cost for the entire nuclear plant to only the turbine, not including the capital required for the hydrogen storage, or the equipment to produce the hydrogen, or the energy cost of the original generation (with large conversion losses). Or, again, the deadweight losses from the safety margin you need for surplus capacity that you might but probably won't ever use, which could double the cost or more on top of everything else. Whereas if you spec additional nuclear it means you're generating that much more useful electricity 100% of the time.
Meanwhile that kind of storage will have more difficulty finding investors, because if it turns out that some cheaper or better alternative comes along, an investment in nuclear might have to average generating power below levelized cost, but at least you recover most of the capital. Putting in $100 in capital only to have the net present value fall to $80 sucks, but not nearly as much as putting in $100 in capital for a complete write off because you were expecting to be selling to the grid 2% of the time when it turns out to be 0% between demand based pricing and better than expected competing storage technologies. Which means higher capital costs (meaning interest rates) that reduce relative competitiveness even further.
