Look, there are three categories of nanny employers:
So wealthy they never ever worry about money—these folks definitely have a full-time nanny basically until their kids can all drive. Along with the rest of the staff.
Wealthy because they have well-paying jobs—these folks may be overleveraged (not at all uncommon in the US, sadly), so even losing only one of their jobs could put them into dangerous territory because they may not be that liquid. These people probably have a nanny full-time because they need the backup care, but if they have other sources of backup care like grandparents, neighborhood SAHM, etc. they mights opt out of the FT nanny once kids are in school. They have plenty but they also look at the cost difference per year between a FT and PT nanny and think about how they could invest that.
Finally there are the families who could barely afford the FT nanny when the kids are little. OF COURSE these people are going to go with a PT nanny as soon as the kids are in preschool/school. They aren’t choosing between PT and FT nanny. They are choosing between PT nanny and aftercare.