(...) whereas fiat not only inflates every year but it will still be strong because the government always regulates it.
The ability of governments to keep inflation under control are somewhat limited and we've seen many cases in the past when the values of currencies were spiraling down uncontrollably. That's why we often see that countries with high inflation have to resort to outright banning their citizens from freely exchanging foreign currencies and putting a halt on crypto trading.
In fact, it is not impossible for Bitcoin to take over the role of fiat currency as a means of payment. (...)
If we're talking about Bitcoin taking over the role of all global currencies or USD (and not just some small local ones) then it is impossible, even considering Lightning Network. Some new blockchain solutions would have to be developed, or a huge chunk of transactions would have to be processed by centralised entities.