Tubes for guitar and tubes for hi fi have very different objectives. Audible distortion for a guitar amp is a desirable feature, not so for a hi fi amp.
FYI, distortion ("overdrive") is not the sole goal or attribute of guitar amps/pedals that attempt to mimic tubes! "Clean" tube tones are as prized as "dirty" tube tones as is the ability of some of them to mimic a variety of amps that are associated with different types of tubes. Some examples include but are not limited to: 6L6/6V6 for Fender, EL34 for Marshall, EL84 for Vox, etc. This seems quite in line with what the OP states:
My thinking is that of a black box with switches and knobs to adjust harmonic distortion to mimic different tube types.