Your general point is correct, but that is exactly the reason that medicine traditionally recommended against vaccinating old and frail people...anything could be the “last straw”.
These days they just want to jab anyone who can’t fight back—without regard for consequences.
I’m not a doctor, just married to one. Vaccines and the elderly always was and still remains a tricky combination.
The elderly virtually always have a less successful immune response to vaccines generally. And, I believe some elderly patient are still steered away from certain kinds of vaccines. Certainly back in the day when attenuated vaccines were more common, it was perhaps a bigger problem than it is now.
Still, I think on balance there have been a number of vaccine therapies developed specifically for the aged over the last decade or two that have really improved the quality of life for this cohort. From shingles vaccine to the pneumonia vaccine, these prophylactic jabs have clearly lengthened the lifespan of some patients and improved the quality of life in many others.