I am against having any way to change your Nymphs, but if it were to implemented, hypothetically, all the suggestions in this thread have been basically free. Cheaper than an upgrade to change a Nymph? That basically makes it pointless to have more than a couple Nymphs. Maybe 4 or 5, some crazy decks with 6, but you could basically play for a couple months and have enough Nymphs to use any combination at almost no cost. The way they are now, it's pretty cool to get one right up until you complete your collection of 6 (or 12) of each, which is 72/144 Nymphs. Or a very long time. If you can change them at will, they probably would stop being interesting at about your 7th or 8th Nymph.
If there was some system to change Nymphs, I think it would have to be on the order of 15,000 - 50,000 electrum per metamorphosis. If they cost the same as 10 or 20 upgrades, any frequent player could easily save up to do it, but you can't just go crazy changing your Nymphs from day-to-day however you please. An upgraded deck right now costs 45000 - 90,000, just for the upgrades. Making a deck cost 30-100% more to include any Nymph you want seems pretty reasonable to me.
I would still be against it, but the way the suggestions are now, they might as well be suggesting that the Oracle give you 1 of each element every time you win a Nymph. You can just go over to the War Auction and see that even relatively new players could easily give up rares and trivial amounts of electrum without even noticing it. You could maintain the emphasis on rarity (which is clearly important since they can't be won on spins) much more effectively if you make the metamorphosis prohibitively expensive.