You mock this medical statement — but it’s perfectly true, and there’s no way around it other than lying.
In many cases, humans do not have comparable biological effects time with lab mice. Take one that you are probably familiar with — calorie-restricted diets and life extension. While humans probably do benefit from them, a calorie-restricted diet will increase a mouse’s life expectancy by 50%. Given that quite a lot of humans spend their whole lives in calorie restriction for religious reasons, we know that the effects of calorie restriction are nowhere near as dramatic as that, or all the oldest people in the world would be monks of one religion or another.
(Or if you don’t like that example, a quick search turns up a bunch of other less interesting examples.)
Given that we’re talking about life extension, studies on this technique would take decades to play out.
More, taking the blood of other humans is not free of risks. There are risks to both the giver and the receiver of infection, allergy, or contamination, and the receiver has the additional possibility of a mismatch. Careful testing will keep these risks small — but they can never be eliminated.
And there’s of course the caustic effect on society of having the rich drink the blood of the poor.
With all this in mind, the FDA is perfectly rational to caution people that the science of this is unclear and there are unknown risks. Any other statement would be desperately irresponsible.