From my experience in the UK you had an individual appointment time of a 10 minute window, in which time you had 10-20 people arrive with the same time, thus limiting people queuing for long periods. Both my vaccinations at a local centre took no more than 25 minutes including the 15 minute observation period, no blood pressure check needed, very short form to fill taking about 2 minutes, another short question and answer from the person giving the vaccine, very efficient.
If you look at Thailand's reported 900k a day and say centres are open 10 hours a day for example (have no idea if correct but just example) this equates to 1500 jabs a minute, 25 a second. UK managed 10 a second I think at best. When you break it down to hours, minutes and seconds you realise the enormity of what's needed to reach those figures. Without proof one can only speak an opinion as to the accuracy of figures. I for one are suspicious of the claims of 900k a day, 500-600k a day, sure, I can believe that.