I love dips too.
Used to do them while holding a dumbbell between my feet till I got to a point where the DB's were too heavy to do this with and started carrying a chain to hang weight from belts with (funnily enough I never carried a belt but would always find an unloved one to use in the corner of most gyms I used to come across).
I do a fair bit of dipping in the 90 degree bend of handrails on the rigs I end up working on, it’s comfy enough and hand spacing is almost infinitely variable!
I think they could be incorporated into SF very well, although the point of SF is to keep things simple - no?
So with not so simple SF, then you could have a list of you’re fave exercises for each movement and rotate them (something I'm considering as I would like to keep track of my abilities in various movements - but on the other hand I don’t want to complicate SF for myself...?)
I used to take a leaf out of "Westside's" ideology years back, and rotate my exercises randomly. It was a great motivator and really made sense (well, of course as they produced so many World class lifters with their principal).
For instance, sticking to the basic SF doctrine of a pull, push and squat, then for you’re 'push' you could use either a push up (various wide to narrow hand spacing, various hand positioning from further forward than you’re head to almost planche-like position way down at the hips, feet flat, elevated, elbows in or out, etc), dip, or chair dip, etc. Maybe the fact that you actually do an exercise and record progress is all that matters? Its definitely better than 99.9% of the rest of the population who just don't bother.
Just food for thought..