I think you both imagine that transfusions are 1 on 1. (1 donor, 1 recipient). In this case, the numbers you present kind-of work out. And sure, a risk of HIV (or whatever) infection versus certain death is worth it in any scenario. (Especially now that HIV/AIDS is chronic and treatable rather than terminal).
Many scenarios involve heavy blood loss and require more than what is normally given by a donor in a single donation. This means drawing on the pool of available blood, so multiple donations will be used of the same type, but they won't be from the same donor.
This raises the risk of transfusing infected blood significantly which is one of the reasons that the screening for blood donation harshly excludes anyone who fits in one or more higher risk groups.
I'm a donor and where I live you can't donate blood if you've received blood (inter-species tissue exchange), lived in UK in the 90s (mad cow disease risk), were born in sub-Saharan Africa (HIV risk) and a couple of others. This includes ever having had male/male sex (very high risk group). Ever been paid for sex? Out. Ever exchanged drugs for sex? Out. The list goes on and on.
The 'in the last 12 months' items are again a form of risk management (they include new partners, tattoos, piercings, infections, illness, surgery, travel to risk countries, etc).
All blood gets tested and though false negatives are still possible, most infections are statistically close enough to 100% detectable after 6 months.
Where I live it's also illegal to sell parts of your body (which includes your blood). The idea behind that is that legalizing this would create a predatory market between people with money and those on the bottom rung of the ladder (poor, addicted, high-risk, all of the above). That's not a hard sell, but it also acts as a filter in the blood donation system. People who are most likely to sell blood are the people you don't want giving blood in the first place.
A detail in my country is that the donation forms don't ask about your sexual orientation, which is irrelevant. If you identify as homosexual (male/male or female/female) but have never had male/male sex, you're good to go.
Blood donation is a region where you're just harshly subjected to selection based on statistics which place you in one risk group or another. Discrimination doesn't factor into it.