I tend to agree with you on the cost for saving. I do not feel like the first version of the second game is hard at all (the other skilled based ones are also not that hard to get the hang off, at least in my opinion). So I do not feel like the game has a high skill floor preventing players from surviving possible bad luck with the RNG elements (and even then you can always restart if you lose the first 5 coin tosses at the start).
So keeping a small cost for saving to prevent players from ruining the tension left in the game feels like a good idea.