I realize it could look weird for certain themes.
How could we make it work? It would sure be nice that Site Identity be better known.
I haven't looked at Theme Identity much, but maybe two possibilities would be a) use a separate Tiki installation in a subdirectory or subdomain here and turn on the feature, and b) just modify theme templates of the current installation to emulate the result of activating Theme Identity and rename them as new themes, like "smartiki-ti.css". I'll try to do some experimenting.