Your link doesn't say that the screenings aren't cost-effective. It says that if you are in a certain age group these are the recommended amount you should do <40: 2-3 years, 40-49: 2 years, 50-74:1 1 year, 75+: none.

Annual screenings were too aggressive, not ineffective.

"In conclusion, the USPSTF reasoned that the additional benefit gained by starting screening at age 40 years rather than at age 50 years is small, and that moderate harms from screening remain at any age...The USPSTF notes that a "C" grade is a recommendation against routine screening of women aged 40 to 49 years."

Note that this recommendation is solely on medical grounds - that is, the medical cost/benefit ratio suggests routine screenings for women < 49 is pointless. They don't even take into account the financial cost.