Once we get the appointment, we can change the booking on-line to a more convenient one (in the cities, anyway - they might be more strict on the islands). I think this is the best approach as it gives people who might not take the initiative a slot, but also allows flexibility to people who need it.
When people are left with the responsibility to book themselves at a convenient time, a lot more people fall through the cracks. Take ante-natal classes, in Scotland you are still allocated a time and your employer has to let you attend. In England, you book your own now and there are much higher rates of non-attendance, so giving people choice also gives them the responsibility.
It is counter-intuitive if you are the kind of person who would get on and book at the first chance you got - but there are a lot of people not like that. There are more people who would show up if they are told "this is your appointment, you need to make it." This is reflected in the uptake rates.