I think that your reasoning here is substantially confused. FDT can handle reasoning about many versions of yourself, some of which might be duplicated, just fine. If your utility function is such that $U(\alpha |\varphi ⟩+\beta |\psi ⟩)={\alpha }^{2}U(|\varphi ⟩)+{\beta }^{2}U(|\psi ⟩)$ where $⟨\varphi |\psi ⟩=0$. (and you don't intrinsically value looking at quantum randomness generators) then you won't make any decisions based on one.

If you would prefer the universe to be in $\frac{1}{\sqrt{2}}(|A⟩+|B⟩)$ than a logical bet between $A$ and $B$. (Ie you get $A$ if the 3^^^3 th digit of $\pi$ is even, else $B$) Then flipping a quantum coin makes sense.

I don't think that randomized behavior is best described as a new decision theory, as opposed to an existing decision theory with odd preferences. I don't think we actually should randomize.

I also think that quantum randomness has a Lot of power over reality. There is already a very wide spread of worlds. So your attempts to spread it wider won't help.

I'm actually very glad you wrote this up, because I have had a similar thought for a while now. And my intuition is roughly similar to yours. I wouldn't use terms like "decision theory," though, since around here that has very specific mathematical connotations. And while I do think my intuition on this topic is probably incorrect, it's not yet completely clear to me how.

Intuitively, one does not want to take actions a and b with probabilities of 2/3 and 1/3, whenever the EU of a is twice that of b. Rather, it might be useful to not act entirely as utility estimates based on the uncertainty present - but if you are absolutely certain U(a) = 2*U(b), then it seems obvious one should take action a, if they are mutually exclusive. (If there is a 1/2 chance that U(a) = 1, and U(b) = 2, and a 1/2 chance that U(a) = 1, and U(b) = 1/2, then EU(a) = 1, and EU(b) = 1.5.)