Employers won't give you papers for visa

Hello!
I'm Brazilian, highly qualified engineer with a good job in Brazil. Despite all that, I hate living Brazil and I want to spend the rest of my life, legally in a civilised and organized country. I always look for job offers in my field (renewable energy) and often there are positions for it. Most applications ask if you have work permit, and most countries would permit an outside worker to have the job if the employer proves the potential worker has some unique skills. The point is, I have never seen any worker do that. Does anyone know why? Is there any liability/ tax the employer must compromise to in order to "invite" an outlander worker?

Typically, the employer in such a case is responsible for obtaining the work visa on your behalf, and yes that typically incurs costs that the employer must bear, along with the time and effort spent on the process.  Also, as you note, they must be able to prove that no EU citizen is able to fulfill the position.

It's a lot of effort I think on the employers part, when in most cases they can just hire an EU citizen without hassles.

Ok, now I see what you mean. I was not sure about all this process, which make sense, otherwise some companies would issue lots of "invitations" to hire skill workforce for lower salaries.... Thanks for your answer.