Why has the European Union banned several airlines?
I think the policy is completely justified. An analogy: You wouldn't allow an unsafe and unapproved car onto a highway in Europe where it presents a unjust danger to everybody else.

You have to remember that the European Union is a fairly compact bunch of nations: To get to Paris from Southeast Asia or Africa, you're probably looking at overflying at least two or three other countries. Thus, a single flight will have wider implications and involve multiple nations. The policy keeps everybody somewhat happy that they have safe airlines in their airspace. It also keeps their own citizens off the airline in question.

I do not think that it is a question of 'caring'. If they do not feel that the airline can safely fly, they ban it. Note that a fair number of the EU blacklist are automatically banned by country if they have insufficient oversight. It's also not a permanent 'thing' or sentence. Garuda Indonesia was on the EASA blacklist for two years until they brushed up, and are now back flying into the EU. Perhaps it might even have been good, since it pushed the company to improve their standards?

Here is a recent quote on the Iraqi Airlines ban:


  ATW understands from unidentified sources that 600 non-EU airlines had applied for TCO authorization. Most had been granted with few problems, but a small number of airlines were subject to greater scrutiny because of their perceived high-risk status. Source


While perhaps less prominent, I think the United States will quickly block any unsafe airline from coming in, although perhaps on a more case-by-case basis. I believe there are other hurdles, such as airport security requirements, that have to be settled to fly into the United States and can act as barriers. I believe the same applies for any other nation.

Other countries say no as well, just perhaps not being as 'vocal': 


  Some Thai-registered airlines earlier faced flight restrictions by Japan, South Korea and Indonesia, following an audit of Thailand's air operations by the UN-based International Civil Aviation Organisation. In June the agency raised a red flag over aviation safety standards and gave the country until November to tackle the issue. Meanwhile, the US Federal Aviation Administration (FAA) last Friday gave Thailand 65 days to address shortcomings it had found. Source