I agree that it isn't necessary for a teacher or HT to do the tour or even actually to be available at the time of the tour. It would be good when tours are booked for it to be made clear to parents what the likely situation is - ie someone from our office will be able to show you around.
It is worth recognising that as someone said up thread, not everyone wants to see the HT or to ask many questions. Lots of people simply don't feel any need to. Fine - the HT doesn't need to see them, however, even they probably appreciate the offer of an opportunity to ask questions if needed.
It would seem a good idea if a non-teacher/HT does a tour that it ends with the offer to either see and speak to a teacher/HT then or that a chance to do that can be arranged at a later point if required. Not to acknowledge that parents may well have questions which requires an academic member of staffs input seems very odd to me.
Perhaps it depends on the school and area. Perhaps in some areas with lots of assertive middle class parents, it is offered, because asking questions is simply the norm. Perhaps in other areas, very few parents have questions which need an academic member of staff to answer. I don't know. I guess some schools simply make a bigger effort to be approachable and deliver a positive outward appearance than other schools do.
I totally agree that teacher/HT leading tours or having chats with prospective parents needs managing so it doesn't disrupt other activities with children or running the school too much. However, the se ALWAYS ways to manage these things to make them work, such as only allowing tours once a term or on fixed dates, or only making appointments for parents with HT after a tour has already occurred with other staff (to establish genuine interest) and then only at times to suit the HT which won't impede other school activities. There are always ways and it is up to the school to manage times and make it work for them, but to provide a chance to ask.
I do not accept that any school can argue with integrity that it is simply not possible for a prospective parent to be able to ask a teacher or HT a question at any point, or through any medium. I would see such a response as totally unacceptable and uncommon.
Unfortunately, what can sometimes happen is that some office staff who take tours can pmake it seem as if this is the case. They feel they are protecting the Head or Teachers...and to a point this is correct, but to deliver a message that it will never be possible to ask Qs of a teacher or HT is taking this too far and would probably horrify the HT.