They do have plans for an enclosure that puts them back on public display, situated back a ways to minimize their stress levels. They're included in the Rainforest blueprints.
Since I grew up in Los Angeles, I remember well as a child going through the old aviaries. They were not a walk-in aviary, but just a series of bird cages basically set up on stilts on the mountainside. My mother would take my cousin and I there every summer (at the least) and because it was such a steep stairway to get up there, she would wait at the bottom while we ran around up there. I seem to recall there were never really many other people up there, probably because of the steep climb and because birds are not that popular. We always enjoyed it, but I think more for the feeling of climbing around a treehouse than for the actual birds (I could not name one species that was there if my life depended on it). Anyway, here is a photo of the last time I saw them, and you can see the bottom falling out as they are literally crumbling apart. They had been closed many, many years before this due to safety hazard.
Just a few species that were found there off the top of my head: Common Hoopoe, Bleeding Heart Dove, Fairy Bluebird, Collared Aracari. Those stand out for some reason. But the list would be much, much larger.
The old aviary cages were at best marginal. When the zoo was first built, the architects who designed the zoo had no zoo experience. They were located on a hill and offered no protection from the elements. A number of species were kept there but as water was used to clean the concrete floors, the wood that held it up began to rot away. Since ther was no funds to replace the wood, little by little the area was closed down. Bleeding heart doves and the first ever Tarictic hornbill hated in one of the lower aviary cages. The entire structure was abandoned when the "new" aviary was built.
