Most apartments do want to ask for your income and verify employment or at least verify you have the income to pay for the monthly apartment rent.
You might find an apartment that would not want proof of income but it may not be as great as the apartment that does verify income.
When you apply to rent an apartment the landlord or apartment manager will run your background through their computer and check for any criminal history as well as see if you're employed.
The apartment manager or landlord will also likely call your work and ask if you actually work there and they may also want an income verification letter.
Your boss or manager would sign the income verification letter to show that you do have the income.
The apartment manager or landlord wants to ensure that they are getting a good tenant who can pay the monthly rent fees and not have to chase them down for the money.