You do have to pay for air if you care what pressure it is at. Non-Sherpas will demand a refund of their ticket price if provided air at ambient pressure at 35000 ft.
Yes, you can increase the pressure. But then your flying tube in a low pressure environment may explode
Or it'll suffer a bigger expansion/contraction with every cycle and hence less cycles or metal fatigue and failure at 37000feet (passenger won't ask for a refund as they will be unable to do)
So the "cabin altitude" is really a balance between mechanical resistance and people not passing out (though this may be a good idea with some passengers)
Result: Each air change costs around .62 of a gallon of gas (assuming perfect efficiency). Or around $2.50 - let's call it $10 to account for inefficiency. In contrast it costs around $10,000 per hour (not including salary) to fly a large plane.
Saying they don't circulate air to save money is ridiculous.
You can work this out my looking at an an airlines profits, and how many flights they did a year.
In this case, airlines are a business designed not to have runaway profit. The unions are very powerful. They know how much money the airline is making a demand large percentages of it. They leave a nominal profit for key investors but shareholders as a whole are regularly left out. In fact, if you look at the entire history of commercial flight, the industry is break-even.
That's not a fluke. If costs were higher, unions would get a smaller cut. If costs were lower, unions would take more.
Philip Greenspun has some great writing on this, as well as the old, shortlived but fantastic Enplaned blog.
By my calculations a smaller 70 passenger plane would use around 1/5 the energy per air change, and they typically fly for only an hour or two. So for an air change every half an hour it would cost them around $4 per flight (and that's assuming low efficiency). So $100 profit is still possible (although I have to say that that's amazing low, but I'll take your word for it).