I agree with random and chris. I think the letter approach has been thorough up til now, and worked for people who were able to plan their days around the appointment (non working people, no time-limited caring responsibilities, possibly furloughed or WFH with understanding employers). However, now it's moving onto younger people, and school/ work/ extra curricular stuff is more normal, I think they will have lots more difficulty pinning people down to their pre-allocated times/ dates/venues. Especially given increasing vaccine hesitancy in younger people and so on, who may not bother rearranging inappropriate appointments. I'd hope these would be followed up later on, but it does seem a bit inefficient.
Lothian in particular seems to have plumped for this random vaccine "hub" approach, rather than using local surgeries, community centres or libraries as other health boards have. So there are half a dozen huge venues scattered across the Health board area, and people are randomly allocated one. At least one is drive-through so if you're allocated that one and you don't have access to a car, tough - you're told to rearrange it online, but it seems hit or miss whether you can get slots anywhere else. There are local vaccine clinics, but you can't get an appointment there if you're relatively healthy, young and mobile.
I've been looking into travelling to my appointment next week (44, Edinburgh). It's the other side of the city to our home, but at least there's a bus to it. I will board the bus outside our local vaccine clinic, pass another vaccine hub en route and reach my designated venue in just over an hour (40 mins before my appt...) It's fine for me as DH can cover school pick up, but really... couldn't something more efficient be sorted?!