I think aluminum is cheaper than stainless, and it is harder to weld. For the most part, TIG's your only real option with aluminum. Even then, you've got to clean off the aluminum oxide layer before welding, because that has a higher melting point than the underlying aluminum. And TIG is definitely more difficult than MIG welding.
I'm not sure how the different aluminum alloys compare with structural rigidity, depending on what you're doing with it, this might be important (building a sculpture, etc.)
For kettles and the like, you'd have to find aluminum couplers or clover fittings to weld to your aluminum pot, and I admit I haven't seen these. Stainless is a far more common substance when it comes to this type of equipment.