Researchers use docking software to run libraries of existing drugs as well as design never-seen-before drugs out of the enzyme protein's active-site pocket.
These operations have been performed extensively this year (by research groups all over the world) on covid's main protease enzyme as well as the spike-ACE2 interface, for example.
My take: Since 0.1% of proteins whose amino acids have been sequenced have ever seen a crystal structure (i.e. the folded model) generated of them. an automated approach to 3D model generation 1) will have enormous implications on drug development, and 2) will most likely come from a new and very different generation of drug developers, who don't have a lot in common with the generation that produced the tweet pasted above.
I found a recent review with some others listed here [2]. It has a nice overview of the process too!
Forgot to answer your other questions. I'm not up to date on the structure-based drug design workflow but back when I did similar work (5 years ago) there definitely were rudimentary systems for generating molecules and docking them. It may have improved significantly since then. But I would probably characterize it as a problem it itself for sure.
Your other question is a VERY good one. Proteins usually fold into whatever may be most favorable based on the sequence, and it mostly stays consistent once it does. However, they are very flexible and structures solved by EM or x-ray crystallography are like a photograph of bird flapping its wings: you will see the wings in a position, and if you happen to have a few birds in the photograph, you might get a sense of where those wings can move to, but it's never going to be perfect. But like wings, proteins usually still have a limited amount of movement. There are other types that are much harder to understand that have less structure, but globular proteins that bind to drugs like this are usually pretty well-predicted by the snapshots we can get.
[1] https://pubmed.ncbi.nlm.nih.gov/10480735/
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6601033/