You can make another currency based off of bitcoin, but it wouldn't have the economic backing that bitcoin does. It wouldn't have the network security that bitcoin does. It wouldn't be worth what bitcoin was worth, because it isn't bitcoin. That's like worrying that the US Dollar will hyperinflate because other countries make their money out of cloth with security features as well.
As for anti-trust, there's no trust or company to go after, just a protocol. That's like trying to break up gasoline burning cars because they're almost a monopoly.
All of these arguments are nonsense.
Especially, by the way, the deflationary spiral one. We've hashed that one over way too many times - learn to search, even just the wiki has a dedicated page for it.
New countries a rarely created or destroyed. Only after major upheavals. So the numbers of "normal" currencies are in more or less fixed supply, even if the quantity of "notes" of each of them isn't.
Cryptocurrencies can be created on a whim, just like bitcoin was.
So I don't think your analogy works.
NB you'll have more success spreading the word if you don't hack the arms and legs off potential converts.
You're missing the point. It doesn't matter if there are more countries, or if there were new countries created every day. Even if they make a new currency each and flood the market with bills, it wouldn't affect the price of other currencies. Same with bitcoins.