It does feel wrong, but it feels equally wrong that the government orders the police to prevent citizen from copying bytes.
The fact that the distribution cost is close to zero is irrelevant.
The problem with copyright is that a big proportion of the price charged is basically cartel/gatekeeper protection money, and has no useful relationship to the true social cost/value of creative work.
Before I wrote book X, there were no copies of book X in the world. The supply was zero, not infinite.
After I wrote book X, the supply was one. Then it grows as people make copies. Copyright law can limit the growth, certainly. (Or enhancement, as the potential profits help promote distribution.)
But copyright law is meant to encourage the growth from 0 to 1 by making it possible to make money from the growth from 1 to N, before the lack of copyright protection makes it effectively infinite.
It's true that plenty of people will write even without getting paid. It's also true that plenty of people wrote because they will get paid. Heinlein started writing to pay off his mortgage.
Copyright law is also the basis for free software. If you take away copyright law, you end up supporting proprietary software distributed only as compiled machine code, not reusable source. This to "impoverishes" the human race.