Except unless you are living in the middle of Bodmin Moor , you are not isolated . Yes it takes only one to infect, but with large crowds , the probability of having that one increases ,and also the severity of the impact and subsequent infection rate increases.
Having large stadia requires people to get there, mingle for a while get the shot and then lurk around for a while and then disperse, travel home and get or give the infection. In my case, I walked down, walked up an empty staircase, sat in a large room with about 5 other people each socially distant, wore mask, went unto other room sat down, injected, by 2 masked people , sat in other room ,even larger with about 5 other people for 15 minutes and walked home. The process would not have been faster in a bigger centre, since all the paperwork has to be done.