A Septim (made of gold) has a value of 1 but a gold ring made out of about the same amount of gold has a value of 75. So basically you are paying 75 gold rings (or more) for one of them.

Melting coins down=unlimited money

You don't have to be an expert in economy to know that would never work.

are Septims pure gold though?

alot of European Kingdoms that used gold or silver as Currency was not pure gold or silver.. in the refining process they mixed it with other lesser metals.. when exchanging Currency, it was based off how much actual gold or silver existed in that nations gold or silver coins

As Funnybunny says, the matter of purity is up in the air... As someone who HAS a Septim (or at least a replica), I'd be surprised if they are gold at all. The colour is wrong...

But anyway, the costs of things in Tamriel are very weird. Despite Tue fact I have never seen a foundry able to produce any noteworthy volumes of metal, forged iterms are absurdly cheap. A longsword should set you back several hundred Septims, and a gold ring? Well, you wouldn't be finding any such nonsense in a shack like the Riverwood Trader...

Basically, you're paying for purity and craftmanship.