I definitely agree with the points you made!
Especally, your last 'disadvantage' point. Whilst screening I think it is important to educate the individuals about returning for follow up screening. A negative result cannot be used as a means of 'the all clear for life'.
I think perhaps, when individuals come into the clinics for screening, it's important to mention risk factors for that specific disease so in this case it would be factors such as unprotected intercourse and mutliple partners.
All in all, cervical screening, as a whole has more advantages to it than disadvantages. (In my opinion)
