Marco Polo was, famously, amazed when he first encountered paper currency during his travels. In this respect he started a long tradition -- why would anyone accept this rather than something tangible like metal. The Khans, it should be noted in passing, solved that problem by sentencing those who refused it to death. Modern states solve the same problem by requiring taxes be paid in fiat -- and, as noted by Semaphore in a comment, by making it legal tender.
The topic is way too broad to go through the details, but basically yeah: there was plenty of debate. (There still is, in fact. If you seek out writings from the libertarian schools of economic thought, you'll run into plenty of gold bugs who are adamant that fiat currency is worthless.)
With that in mind, you simply cannot compare the two. Crypto -- or at least BitCoin -- has a very low transaction rate, which rules out general use. And current mining operations, which are necessary to conduct transactions, consume more electricity than Denmark. It might have some uses down the road but it's simply not the future.