Why should a cryptocurrency replace existing payment systems? This will not happen anyway. The states' cash may still decrease in volume, but is unlikely to disappear in the near or even distant future. However, non-cash forms of payment are now very convenient and will simply improve in the course of competition with cryptocurrency. In general, it is expected that the cryptocurrency and non-cash money of the states will exist in parallel and, most likely, in the future we will see their combined forms of circulation.
There's a possibility that both crypto and Fiat will co-exist for a long time. However, with the rising popularity of Bitcoin, it's widely possible that crypto will render traditional payment processors obsolete. Of course, Fiat will always be there as it's backed by the government. But in the case of traditional payment processors like PayPal and Western Union, they may not survive in the future if they don't adapt to Blockchain technology.
People would rather stick to a system that's virtually free and speedy at the same time. Bitcoin compared to other payment systems, it's still the cheapest and fastest one in existence. While it's still facing scalability issues, the Lightning Network is being developed behind the scenes. Once it's finished, people can enjoy instant and near-free transactions around the world. In effect, this would allow many people to switch from traditional payment systems back into cryptocurrency.
Despite this, there will be many forms of payment (as you've said earlier). This means, that aside from Bitcoin, we'll continue to experience a world where people deal with Fiat, Gold, and other means. Hence, Bitcoin or crypto cannot be the only solution to everything in the world of finance. Just my thoughts