That doesn't make any sense... How does having one screwed up system justify another? Maybe we should start paying twice for groceries too, because we pay twice for toll roads and research papers...
1) The new road is 60% in the public interest and 40% in the interest of its users, so 60% is paid with taxes and 40% via tolls.
2) Society feels it's reasonable that all children, regardless of family income, should have educational resources. 90% of school is funded by taxes and 10% funded by fees paid by students' families (lunch, field trips, books, etc.).
Speaking generally, paying for someone else's profit is essential to the free market. Without profit, much less would get done.
Speaking about this case in particular, knowledge, at least much of scientific knowledge, should not be sold at whatever prices the market will bear, which is what these publications seem to be moving toward. Imagine the prices you could demand for knowledge of immunizations, relativity, DNA, law, history, etc. (if they weren't already publicly available). Imagine the disruption to science, to the advance of knowledge, and the incredible cost to humanity if only a few with enough money could access these ideas.
The second payment is for you only, because you are getting specific and temporal value from access.