If 100% of the population is vaccinated, and the vaccine is 90% effective against catching it, and 95% effective against hospitalizations, and 99% against death, then
100% of people catching it, hospitalized and dying of it are vaccinated. In other words, the more of the population is vaccinated, the percentage of vaccinated vs. unvaccinated cases will go up, but that doesn't indicate it's any less effective. However, the fewer number of unvaccinated folks around not only helps stop the spread because there are fewer people susceptible to it, it stops the likelihood of another mutation that is even more deadly, or worse, one that renders all the vaccinations of the 171 million who already have it, useless.
Also, I don't know who told you the CDC stopped reporting breakthrough cases (I have my suspicions), but you can go right to the CDC website to see that's not true.
https://www.cdc.gov/vaccines/covid-19/health-departments/breakthrough-cases.html