Yes vaccinated with pre-alpha, alpha, and delta have faster viral clearance... but what about Omicron which is 99% of cases now? Maybe the study was done too early, but the results are very bad for vaccinated with Omicron.
"In other words: out of 100 boosted persons who catch Covid, 31 — or one-third — will be still carrying LIVE VIRUS on Day 10. Out of 100 unvaccinated persons, only 6 would test positive on Day 10 — over five TIMES fewer people." [1]
So even if you justified treating unvaccinated differently due to viral clearance (completely disregarding that prior infection, age or weight has much more influence), eventually you'd be wrong using that metric anyway.
[1] https://igorchudov.substack.com/p/study-boosted-people-slowe...