I think that the need for deodorants in daily hygiene and grooming depends on the person. A lot of people don't realize that bad smelling armpits are not par for the course. Fungal infections can crop up without us realizing it.
If you change your razor often enough, or wash it thoroughly, you can better avoid such infection. A few drops of Colloidal Silver placed on a cotton ball can be a gentle way to get rid of fungal infections in the armpits. Colloidal Silver can actually help cure a lot of ailments, as long as you don't consume too much...because too much can turn you blue. And no one wants that.
The need for deodorant also depends on body weight and level of physical activity. A small, very thin woman who works in an air conditioned environment and doesn't do a lot of physical activity could probably get away without using deodorant in her daily hygiene and grooming routine--given that she still showered often. I am of medium weight and practice hot yoga...so I DEFINITELY need deodorant. I use Tom's Natural Deodorant, but there are a lot of great ones out there without Aluminum or dangerous chemicals.
Thanks for the interesting question!