Cervical cancer screening is currently recommended to begin within three years of first vaginal intercourse, or by age 21 regardless. Women in this age group are not the ones most often diagnosed with significant cervical precancers or cancers, though, and women in their 30s and 40s are the ones primarily at risk. HPV infections and cell changes in younger women tend to clear readily, which is why HPV DNA testing is only approved for routine use in women age 30 and older.
Younger women do need to get into the habit of Pap testing, though, no doubt about that. They also are the ones primarily in need of the HPV vaccine (currently approved for females through their mid-20s). Also, sexually active women under age 26 should be screened yearly for chlamydia.
I think the focus should be on prevention: 1) HPV vaccines during adolesence; 2) Pap testing shortly after beginning sexual activity or by age 21; 3) awareness that young women are at very high risk for a number of STDs, many of which don't readily cause symptoms. About 10-20% of women with untreated gonorrhea and chlamydia, for example, will experience pelvic inflammatory disease as a result, which could lead to tubal pregnancies and, potentially, infertility.
Hope this helps!