I've seen plenty of glass and acrylic aviaries sold... mostly large cages like aviaries designed to go in nursing homes, ect. Since birds can't climb on the sides there is less functional space for the birds so you really would need a larger cage than you normally would. I think a large glass aviary with some silk plants or other items to hide in is fine for finches, small softbills, ect.
Parrot Island (a parrot supply store) used to sell acrylic cages designed for parrots, although it looks like they only sell carriers now - they were acrylic with large slots to allow airflow and some climbing. They didn't look too bad but I still think cages with bars are better for most parrots, if only for the extra climbing.