In most quantum computer designs, gates are signals generated on demand at runtime rather than material deposited at fabrication time. In this regime, the concept of an ALU makes no sense. Instead of just sending pulses doing the exact gates you know need, why would you instead expand that short sequence into long sequences that emulate potentially applying every arithmetic operation to every input and then mux out the result you already knew you needed. It's a lot of extra work for the same final result.

A quantum ALU would also be substantially harder to design, because of the need to maintain reversibility. For example, every operation would have to run as slow as the slowest operation (or else the timing side channel would measure which operation occurred).