There is no way storing the spent fuel would cost so much that it would generate 38c/kWh of costs.
For example the total lifetime costs of Onkalo (Finlands spent nuclear fuel storage site) is estimated to be 3.5 billion.
Lets take the new OL3 reactor as a example. It produces at 1600MW which comes to around 14 million MWh in a year so 14 billion kWh per of electricity produced yearly (slightly less in reality with downtimes for refueling and maintenance). That would mean that if storing the spent fuel would actually cost 38c/kWh just OL3 would generate ~5.3 billion euros worth of fuel storage costs per year which is more then Onkalo lifetime total costs. And OL3 has a planned operational life of 60 years.
And Onkalo is supposed to store all of Finlands already produced spent nuclear fuel and the fuel produced in the next 100 years.
Even if you add dismantling costs of the plants at the end of their lifetime there is no way to get to such crazy numbers even if it costs 2 or 3 billion euros per reactor to rid of. Lets say with 60 year lifetime of OL3 you get around 840 billion kWh produced and decomissions costs 5 billion it would be ~0,6c/kWh of cost. Yes it costs but not tens of cents. For the older plants that produce less it would be around 1c/kWh.
In Finland they started to collect money into a fund for decomissioning and spent fuel storage in the 80s and it currently has a bit over 20 billion euros in assets (the fund invests the money on markets so it fluctuates obviously). So basically they try to do their best to estimate how much money they need to save and collect it during the lifetime. For now it looks like the amount has been roughly correct. And still the for profit companies keep investing into new nuclear plants with this cost already in the price so it doesn't seem to be too much.