I never thought exchanges were making money by selling data.
That's virtually their business model. In the modern world exchanges have 3 things on offer standardization, order entry & market data.
The final 2 are how they make their money.
The final 2 are how they make their money.
The more granular or quickly you want the data, the more it will cost. In addition to paying for the initial data, you are not allowed to redistribute the data, in real-time or historically, with out paying royalties to the original data providers per user.
This creates a complicated accountanting system for data delivered to end users of the data.
Aggregate market data vendors (Factset, Bloomberg, Activ) pay for the initial data and then pay per user/query/etc...
Some data becomes available for unlimited distribution based on licensing, usually this data is time delayed and not allowed to be queried for historical analysis. You'll often see things on Yahoo or Google Finance that say "market data delayed by 10 min".
One of the most common sources of this delayed data is yahoo and there are open APIs for querying it. Usually in Python or a statistically language like R.
Interactive Brokers has an API you can add to your brokerage account for programmatic access across multiple exchanges. Which provides market data and order entry.
If I miss understood you, and you are interested in a open API standard for financial data there are several FIX, ITCH and OUCH are some. But they are almost always forked per exchange and sometimes even per product.
tl;dr It's not the API or infrastructure that costs, it's the data itself.