Nope, I suspect you're not looking at WHO it is costing.
It's profitable FOR THE PAPER COMPANY because they're making more money from selling what they recycle the paper into than they're paying for the old paper coming in.
The problem is, the municipalities collecting the garbage paper to recycle are likely spending more money collecting it and sorting it than they're taking in from selling it to the paper company. This is where the money is lost and how NYC can save that much $$$ from stopping recycling.
Paper can be profitably recycled in cases where the collection and sorting costs are minimal, as it typically is with "pre-consumer" waste. If a company has a ton or so of unsold magazines that can be thrown in bulk into a pulping machine [assuming the machine doesn't mind stapes] that may take a few minutes of labor and generate a buck or so of value.
Compare that situation to one of collecting newspapers from a recycling bin; that requires either having workers shake out the individual newspapers to ensure there's nothing else mixed in with them or else accepting product spoilage resulting from mixing in unsuitable stuff with the paper. Managing a ton of paper that way is apt to require man hours worth of work and thus be far less worthwhile.