I think that it is for this reason, the world governments, especially the USA, being against privacy, that Monero would probably not be as widely accepted as Bitcoin, but that's not to say it won't be more widely accepted. It think Monero potentially can become as widely accepted as Litecoin.
The sad fact is that nobody cares about privacy. People are fat and complacent sheep. I asked all my friends and family to install an encrypted text message app and guess how many actually installed it? ZERO. It is a very easy to use app (Signal for iOS and textsecure for Android) so I don't understand why they won't do it.
I can understand not using encrpyted PGP email, even I cannot figure out how to install and use it!! But textsecure and Signal are easy to use, just like normal text messages.
Even in the American revolution, only 3 PERCENT fought or supported the revolution against the British. The other 97 percent just didn't care. Today, the percentage that just don't care is probably 99.9 percent. I remember, during the Vietnam war, there were massive anti-war protests. Where are these protests against the fighting in Iraq and Afghanistan now? People just don't care.
That's why Snowden is a martyr and a superhero. Honestly, if I were him, I would've just shut up and accepted my $300,000 USD per year job working for the NSA. People just don't care about his sacrifice. He's basically under house arrest for life. For what? For the masses who don't care if they are enslaved sheep.
Anyways, my point is Monero will never be the next Bitcoin, but it could replace Litecoin because most people don't care about freedom and privacy. They just want to get fed, drive nice cars, and be fat and happy. Monero could increase greatly in value, maybe 10 to 20x in value, but not 1000 times the value.
P.S. Understand that this is not a knock against Monero. I like it a lot. I am actually programming an app for Monero for people to buy and sell stuff, just like ebay, but better because I want to offer services, too, not just the sales of goods. In order for Monero to be accepted, we have to be like Amir Taaki and code apps that increase the demand for Monero, just like Amir Taaki did for Bitcoin. I think Spagni's (fluffypony) new dice gambling site for Monero is a step in that direction.
The purpose of xmr is to protect one's privacy. This is at least my understanding. I dont view monero as a bitcoin killer or even a litecoin killer. Its there with one main purpose, to ensure everone a right to privacy. Not everyone cares about privacy. So bitcoin is not going anywhere anytime soon. But there are people that value their privacy. For them monero is a perfect solution.
Also, there is no reason to use monero for tax evasion, or to think about it as being desing for this purpose. In monero you have view keys, to disclose the transactions when needed. So a merchant or a person can keep their transactions privet from other merchants or people, but be fully transparent to tax office to which he/she can provide its view keys.
Companies and governments determine what money they accept, and what company or government is going to want a money that links them to all their activities for all time?
Yes, companies and governments decide, and they will not allow anonymous or even psedoanynomouse cruptocurrency to be "officially" used which is not controlled by government/company.
In Russia, for example, they already want to
launch their own cyrpto, approved by government. The "BitRuble will not be pseudo-anonymous like bitcoin due to the aforementioned Anti-Money Laundering (AML) and Know-Your-Customer (KYC) policies pursued by the regulator".
Its super easy for government to force ppl to use their 'own' cyryptocurrency. Its enough that they will pass laws requiring merchants to accept NSAcoin or whatever coin (or employers to pay salaries with such a coin) that the government can track and control.
Not every country will do this. Some countries that care about privacy (like Switzerland or something) might go the opposite way and embrace something like Monero in an attempt to attract privacy focused businesses (like shapeshift) who are seeking a new home.
In the future people may immigrate to new countries for privacy reasons.
Under the USA and EU pressure Switzerland has modified its legislation. They offer no more numbered accounts and they exchange client datum with USA and other countries.
Other offshore countries also begin accepting AEOI rules under USA pressure.