Red blood cells aren't part of the immune system. We're talking about the white ones. The immune system ages and senesces through cell division, and that's the one of the main drivers of our life expectancy. We have a programmed death at no more than 125 years of age, as our immune system senesces and becomes unable to clean up cancers the way it used to. Adding a young immune system into our veins is a way to partially cheat that limit.

Then perhaps you can direct me to the study that has measured the effects on blood draws on life expectancy down to the week.

It's impossible; we don't have the technology to measure anything down to the week. So we have no idea what the real numbers are (which is why I said "maybe, say,").

But we do know that there are numbers - repeated blood transfusions from young to old will increase the life expectancy of the old while reducing the life expectancy of the young.