I am guessing that starting vaccinating at 65 in the way that they are is the simplest method, the one that will take least planning and therefore be cheapest!
The alternative of vaccinating at 69 for a year, then at 68/69 etc. until they get down to 65 sounds a bit of a nightmare to me.
Supposing that people of 65 are likely to benefit just as much from the vaccine than the 66 - 69s, and the NHS either can't afford, or dont have the personel to vaccinate all 65 - 70 year olds in one year, (I don't know if that is the case), then it probably makes just as much sense to do the 'easiest' thing of doing people at 65.
But I can understand why people who have just missed out now annoyed. I would be too in that position.