Background

Last night, I debated a friend of mine about the decentralized nature of bitcoin. He made an argument indicating that the Chinese Communist Party isn't concerned about bitcoin because more and more bitcoin transactions are completed in China and he believes the Communist Party of China is behind these mining farms. He claims that once all bitcoins are mined, with China owning as many mining farms as they do, they can charge a tiny fraction for every transaction they process, thus making a stable bitcoin revenue over the long run. His point is that it's in their inherent interest for bitcoin to become important for their citizens to use, as it's a small tax on all the usage.

This is his way of explaining why China, unlike Russia, hasn't made bitcoin illegal for citizens to use (even if the citizens are trying to hide capital). I was not aware that a miner processing transactions could charge a small fee.

Question

Can a company/country set up a mining farm for processing transactions and charge a fraction for every transaction, say 0.0001 bitcoins per every transaction it completes?