The common application just means you don't have to fill out unique admission forms for every school. You still pay an application fee to every school.

In some other countries there's a national system with a single modest fee. In the UK this is 'UCAS'[1], a nonprofit org. You apply once, and indicate your top N (say, 5) favorite school+program. The applications are sent to the schools, and they can make you an offer.

If not accepted for any of them, there's a follow-up matchmaking service (called 'clearing' in the UK) to help find an unallocated spot.

[1] https://en.wikipedia.org/wiki/UCAS

From the common application site: While some colleges may charge an application fee, others have no fee to apply. And, many will offer fee waivers under certain circumstances, including financial need, veteran status, and more.

Based on a conversation with my nephew who applied to a double-digit number of colleges this past year, the application fees are apparently more the exception than the rule these days.