The problem (well, one of them) is that you jump from "The long lived isotopes are broadly uranium and plutonium" to "uranium and plutonium are fuel, and anyway it's just alpha radiation". That COMPLETELY ignores other long-lived fission products; Zr-93, Tc-99, Pd-107, etc.
There are a variety of other errors in your claims. For example, oxygen does not have an infinite half-life; SOME isotopes of it do, but others do no.