If I want to aggregate payments for many vendors, how could I profit by running my own payment gateway without third parties?

If you don't want to go to a 3rd party, you can become a financial intermediary for these transactions, by being a processor yourself. This varies from country to country, but in most cases you would become a principal member of VISA/MasterCard and then associate yourself with an acquiring bank to handle your acquiring & processing business.

Though I have phrased it very casually here, there is much more involved in becoming a processor. There is a good primer on all the facets of becoming a processor as published by WePay: Page on wepay.com