While it is certainly possible that will happen in the future, the question how will we get there?
From a non-investment perspective, lets focus on 4 main issues:
1) Lack of volatility
3) Acceptance by businesses
2) Acceptance by users
4) Non-interference by governments

1) Lack of volatility is a no-brainer for any successful crypto to be a reliable means of exchange in regions with economic stability and banking.
Sure, we have stablecoins (fiat-backed, gold-backed, basket-backed, algorithmic) serving as a bridge for exchanges, but at present none have enough scale to replace a regular fiat currency (liquidity-wise) nor have the transparent governance mechanisms to resist systemic shocks (trust-wise). Libra, if it works as envisioned might actually work on this front.
2) Use and acceptance by businesses (merchants) is quite a crucial factor often overlooked by our community. P2P transactions, volume and liquidity are great, but if no outlet accepts it, you still need to convert through an intermediary. Payment provider integration is likely to be the case forward here, as accepting on-chain payment is not cost-effective nor scalable to multiple chains (plus connecting to exchange to manage balance sheet).  It needs to happen at scale, ruling out small shops as enablers of scale and entering the territory of medium-to-large business. At that level the bottleneck to decision-making process is compliance department and top management. A compelling business reason needs to be presented why they should integrate a new provider, with expected revenue increase. The best way forward here is to support a crypto-payment provider that provides the best service and helping them grow. This can be done by constantly nagging your favourite business to integrate provider XYX (not a specific currency like BTC). This will be a long-term effort and the community really needs to step up on this.
3) This ties in with the previous one. If a business adopts a new payment provider and sees no usage, they will drop it and mark it as a failed experiment. Usage by mainstream users is crucial, generating "sales" volume that can maintain the option compelling. Having a great UX and consumer-friendly is also key here (think of PayPal and their refund protection. If I get scammed I want to contact someone and get my money back. If this is not possible, I'm gonna leave a bad review on the merchant and we all know business LOVE bad reviews).
4) This one is the one we can least influence, but quite important for business acceptance. If governments pass regulation clarifying their stance on cryptoassets (not all are made alike), especially payment-oriented tokens and corresponding tax treatments, this will gradually erase the negative ecosystem connotations and decrease risk of adopting new technology.

Just my 2 cents  Might be wrong though 

Who thinks that it will be replaced in the future? Me, I don't think so.

It is true that I like to use some of my cryptocurrencies most of the time but I don't think it will be used as a currency, it will stay as it is even in the future. Some countries may create their own cryptos but not replacing their fiats since there are still a lot of other things they should develop and improve other than cryptocurrencies.

For me, its way to long to make crypto replacing fiat, Yes let assume that all government sees that advantage and capability of cryptocurrency but this government sector will just allow cryptos to their state and will not take to much action on it. The different nation has different problem and priorities, and I think they need to much effort to make it possible that crypto will replace fiat. Also, I feel that they will just create their own crypto and will not replace their currency/fiat.

Cryptocurrency is a asset.
How it can replace fiat?
Only the stable coins can replace the fiat currency.



This debt based currency is best way to keep economy up and running.




Bitcoin and Gold have Zero value!



Gold and Bitcoin are nothing without fiat currency.
Im sure the Fiat currency like we have Today the debt based currency will stay for long time...


The New Era Will be Stable Coins.

I know that enough problems will be predicted when crypto replaces Fiat. in terms of potential, I think crypto does have the potential for it. we know that quite a lot of electronic payment instruments are replacing fiat at the moment, I think that crypto can be like that.

In addition, although many reject the use of crypto as a transaction tool, many governments support the development of crypto as technological development. however, people nowadays sometimes use crypto as a transaction tool.

Well, I only see the potential, whether it will succeed or not in the future, and I also realize the various contradictions about this.

In order for everyone to find out how much money is in your wallet, you must first disclose your identity and the wallet associated with it, so I do not see a problem in this.
I don’t see the future where there is only cryptocurrency, because some projects are simply not needed, some may turn out to be fraudulent schemes,
or just be caught in something that will lead to a drop in the price of this coin.
Which will remain for people who have most of the savings in this coin ?
It is very dangerous. And most importantly, the market is excessively volatile, this has led and will lead to hard falls. Nobody wants his assets to decrease by 90%, the expectation that they will ever grow back turns into torture. Imagine how many people have been waiting for the return of Bitcoin to the mark of 20,000 and the growth of altcoins with it since the end of 2017.

Indeed, we simply need to look at a series of developing projects in this market, compare the value each month, sometimes we see the times when the value is at its peak, sometimes it will is the despair of investors, crypto has a very fast fluctuation rate, holding crypto is similar to holding bubbles, we cannot know when it will fly or explode. And back to fiat, this tool is for us to use every day, it does not move beyond any control, crypto want replacement is one thing that will be rejected immediately from the community

Cryptocurrency does not intend to replace fiat. Cryptocurrency was designed to bring financial independence to its users thus it takes the power of control the governments have over the financial transactions of the people and gives it back to the people. Since the fiat has got the full support of the governments, it will be very difficult for cryptocurrency to replace it. Both will rather coexists as the governments cannot stop cryptocurrency as well.

indeed it is very difficult to happen. after all, if that happens, one of the problems we face is that it depends on the internet. That will make transactions made in difficult areas of the internet network will make it hampered. besides, in the security system, I think it's quite risky, especially if we store all our assets on the hard wallet. if it's gone, then it's very difficult to return it, or even it can't.

Fiat currency comes from DEBT
Debt is liability, responsebility.

The Debt Gives value to Every dollar or Euro.


Now Let's Say we Don't have debt, and You are Federal reserv or Central bank, You need to provide your currency to People to use it.

So how u gona do that?
You print money, Right?  But how do You Know how much?  Let's Say the population in Country is
900.mil so will You print half like a 450.mil?
That means half People must be in absalout Poverty!! 
Right You print 800.mil. It means 100mil. People must be in absalout Poverty!

So You print exacly 900 mil. Or more  So then If Everybody Will have enough money or more then the money Will have no value!

Debt is Liability so the debt intrest Will make People to pay Back more then they Got... So Principal plus interest,  so People Will start fighting with other People in order to pay Back loan that what Gives value Now to Fiat!




Cryptocurrency... Is debt free, then it Can be Only with value When its less then People.

In this Case the cryptocurrency Can be Only currency in the World When are Only  rich and poor!

The Debt is Only factor what Will let Everybody to feel rich buy the things what they Can't afford.


If the cryptocurrency Will be world currency we Will have full communism Regime or Even totalitarism of fullest