Cooties are body lice, unlikely to exist in a carpet that is cleaned properly.
My guess is you are speaking the term more broadly, such as the fictious childhood germs that little boys think they will get if they kiss little girls.
The point is of interest, though.
As a landlord, I routinely have properties cleaned, painted, and the carpet cleaned. In our humid climate, though, if the tenant was less than clean, and especially if they had pets, I replace carpet.
On the other hand, knowing what I do about what cleaning can (and can't) do, I'm still confident that I can rent out a home with installed carpet that has been cleaned and treated with a sanitizer as a part of the process, and do so in good conscience.
Such things cross my mind when I stay in hotels, believe me.