It is said that bitcoin will destroy the fiat system but i believe that if this happens the world will change completly because banks and a lot of things will go out of market.
I don't believe on what you have said. Governments cannot just let the fiat system get rid easily. If that happens, it will cause a big uproar. Implementing new systems will be difficult. So I think there will be two systems at the same time: the system for currency and the system for digital currency. Bitcoin depends on the demands. So it depends if almost everyone know bitcoin.
It can havr more users by 2022 , many will get interested on it especially now that ICO advertising were almost seen the most used apps and websites. By then it can get more users. Now many counyries implementing it ,soon there are more additional.
There is nothing wrong in predicting that bitcoins will have so many users by 2020. With every passing minute, the number of users is increasing and by 2020 bitcoins will be among most used currencies. Bitcoins are already famous worldwide, so they wont face serious hurdles to be known by maximum people in 2020