As soon as you want an aero wheel, you are looking at carbon, no? I am not aware of really deep aluminum wheels. I have heard that in the past there were hybrid wheels where you had an aluminum rim with a carbon aero faring on top.
And the reason that many carbon wheels are stiffer is basic physics: the rim is like a tube, and the larger the diameter, the stiffer it is.
That being said, my mountain bike has high-quality aluminum wheels from Stan’s with XTR hubs and they are excellent. My XC bike weighs less than 10 kg even though it has a mid-grade carbon frame and aluminum wheels.