Burn out in clergy is high in the 40 plus age group.
It is possible they are being careful to avoid this
My dh is a vicar and takes Saturday as his day off when possible. He has 4 this half term due to other things :(
He has to be very careful to preplan his time to get a day off, to have time off one evening a week and an hour at some point in the day when he has evening meetings
He has 4 churches and a diocesan role to fit it (all normal these days) and in the future more will be added. He has to delegate now as if hs doesn't he will be more stressed and be worse of when more is added.
It is possible your vicar is not doing enough - it can happen, but more likely they do more behind the scenes which you don't see
When I was a vicar I found certain things very emotionally draining, the politics and meetings more than the pastoral care. Each person is different and finds a different way of coping.
It is important a vicar has a hobby or volunteers somewhere else. This may mean being careful about days and time off
The way churches are run is changing everywhere, more is being done by the people on the ground as the leaders cover a bigger patch or number of people.
Hope this helps shed some light :)