" I think the straps help retain the kites shape, but if you get the skins just right they dont need to do this?" -foilholio
Every CAD-design program can produce geometrically correct shaped skins. Problem is when ram air pressure, altering cell height/width ratio chordwise, different loads and fabric stretch affect how cell balloons in practice. These are quite messy things to master in foilkite design. Parameters like skin tension and "D C Ballooning" (?) control are used to counter unwanted things, to make surfaces more aerodynamic.
Inner straps which take spanwise loads are good because they let lower skins balloon freely, smoothier.
What you wrote FS's development in foils I mostly agree. P4 really was an advanced design, but its bridle is not shortest possible by far. But it is okay. I think it tried to compete with LEI's, but get caught between them and Speeds. It is quite rare kite nowadays, it wasn't big seller ever.
I don't fully agree about jet flaps. They have drawbacks, of course. But it is valuable goal to try to get backstalling later, like it is on LEI's. Many kiters just want to sheet in and go. That kind of kiters often choke foilkite and then think foilkites suck.
Did you check my "Speed6"? It has much more cells than A15 or two or four more than current Speeds, but less total bridle lenght than in any of those. Still, every rib is fully supported. Of course there is limits how short bridle can be, it must not be too short.
Cell count 43 is very good compromice between bridle simplicity and good enough cell width/height ratio for a kite with AR over 6. If more cells, bridle becomes more complex. If less, cell shape gets worse. I am really pleased with that quick design, one of my best (at least on paper), I think