How long do you predict it will take for the day-to-day volume of crypto assets to surpass that of fiat currencies?
IF the blockchain succeeds, I wouldn't expect to see a potential flippening to happen before 2025-2030. The current level of real world usage for the blockchain is very similar to that of Graphene - "Graphene can do just about anything, except leave the lab".
To use some analogy, Graphene and the Blockchain tech can both do a lot of wonderful things - both are wonder technologies with extremely high potential applications. With both Graphene and Crypto currencies, we know that the underlying potential is huge. However, the challenges are also there. First, you have to come up with a way to use these properties for beneficial applications. Then, you have to scale fast enough while keeping it low cost, which so far hasn't been the case for most cryptos including bitcoin(tx fees,scaling issues) or graphene(high costs for large scale productions).
Even though none of us currently use crypto for day-to-day purchases, the market cap is very high - which is all due to pure speculation, or what I would call, emerging market value. Its the market that determines ubiquity or obscurity of technology, and it does not care how a technology works; it cares about what problems that technology solves.
If the blockchain tech succeeds in solving the issues facing fiat currencies both physical and digital, one thing is certain. The market cap will grow hundredfold, and it's going to imitate the stock market as a device for transferring money from the impatient to the patient. So HODL

Exactly, I know that blockchain is here to stay and it will happen soon enough. I'm glad you somehow make an analogy about Graphene and the blockchain tech, and it will certainly bring many opportunities in today's technology. I have been eyeing a lot of projects/companies that have been adapting it. This
have done scientific research that shows, the graphene foam obtained by their Science Team and it shows great potential in its application in high power lighting devices excited by microwave techniques. These devices are characterized by emission efficiency that allows them to be applied in street lighting or lighting large areas such as sports halls. It's really amazing how far we've come and I'm glad we keep evolving for the betterment of our society!