When my DC had Orthodontist appointments , if someone wasn't there , the receptionist would phone them. Unless they were at the point of walking through the door , they were a DNA.
They also only allowed after 3pm appoints for Yr 10/Yr11 , so if your child was younger , the parent had to arrange time off to accompany . And parking was rubbish as it was in town.
I work in NHS , we have a 10 minute late policy . But TBH , it is far more hassle for me to argue/reason ( we don't have Receptionist )
If someone is late and I was to say I wouldn't see them , the answer would always be "Well I'm always kept waiting"
It creates a nasty atmosphere
I will see someone then if they don't mention it , I'll say at the end "Now you know you were late today , a lot of my colleagues won't see you if you're 10 minutes late . I saw you but you won't get seen if you're late again"
We do have the repeat offenders though who are always late and come in with a "oh what am I like " attitude .
Taking the next one in only works if the next one is there !
If I am waiting for someone and the next patient is keen to nab there space , I will wait a bit . The patient might be bustin' a gut to get there . If they are pushed out of their time slot they might think " why should I bother "
And the ones who phone up to say they'll be late - It Does Not Stop Time 