The search argument can be debated. An agency will tell you it targets different keywords for each client, and sometimes that is even true.
The advertising argument cannot be debated, because it is arithmetic.
谷歌广告 runs an auction. What you pay for a click is determined by who else is bidding on that keyword at that moment. Add another advertiser to the auction and the clearing price rises — for every advertiser in it, including the ones you already represent.
So when an agency runs Google Ads for four clinics in the same specialty, bidding on the same treatments, in the same city, it has manufactured its own clients competition. Their cost per click goes up. Their cost per enquiry goes up. The agency bills all four of them for the privilege, and its revenue goes up.
There is no version of that arrangement where the clinic comes out ahead.