That's not what the article says. The CMA is intervening based on their plan of replacing cookies with Topics (née FLoC). If they just wanted to drop 3p cookies without a replacement, they could.
The CMA has specifically mentioned that just blocking 3rd party cookies would provide Google an unfair competitive advantage because their large web presence allows them to develop better user advertising profiles based on just first party information. Advertisers without a large first party user base (because they only do advertising) would not be able to develop user profiles.
The whole privacy sandbox effort it's supposed to level the playing field between large content providers that are also advertisers (Google, Facebook, etc) and providers that only do advertising (Criteo, RTBHouse, etc). Google couldn't drop 3rd party cookies support without Privacy Sandbox.
[0] https://www.adexchanger.com/marketers/the-uks-cma-wants-ad-t...
That's debatable, but I doubt that's the case. The CMA isn't a privacy organization; they deal with monopolies. They're intervening at the behest of other advertisers who are concerned that they'll lose the ability to adequately track users under the Privacy Sandbox proposal. The CMA's chief concern is that everybody is on equal footing.
The alternatives proposed for more private ad targeting have gone through multiple evolutions, including FLoC and Topics, but these were created largely in response to the CMA's objections.