Recasting another voice actor would have the effect of causing those watching the new film to remember the old one all the more while they watch it, and that might not be the best way to go.
Letting the new Aladdin stand on its own and be its own thing is likely the best way to achieve success.
Certainly, bringing Gilbert Gottfried back would have been a big nostalgia move, but that might also be exactly the reason it didn’t happen.
With Will Smith coming in to voice the iconic Genie, that character, and thus the entire movie, is going to have a very different tone and feel.