> In most cases the proteins were determined to be interesting by other experiments, and then people decided to try and solve their structure.
Yes, that's what we're doing right now, because structure is not a useful predictor, because we don't have structure available in advance of studies on the protein itself. There was no point to a "functional taxonomy" of proteins, because we were never trying to predict with protein-structure as the only data available.
In a world where protein structure is "on tap" in a data warehouse, part of the game of bioinformatics will become "structural analysis" of classes of known-function proteins, to find functional sub-units that do similar things among all studied proteins, allowing searches to be conducted for other proteins that express similar functional sub-units.