Coming from an organ building background, the first picture really says it all for me.
Those squares are adjustable and therefore prone to inaccuracy and were never considered a good enough tool for the precision work that was involved in organ building and back then, no self respecting organ builder would have used one in place of a precision square. They just weren't thought to be good enough.
Without wishing to offend anyone, the way I see it, they're good enough for what I'd consider rough and ready joinery, I even have one myself which to be fair is pretty decent but, for precision and where accuracy is to be repeated and essential, then a good quality square simply can't be beaten. I use mine as it happens for setting out/marking out much like a marking gauge for which they are very useful and even for unimportant/rough squaring but for precision squaring no, I have other squares for that job
The fact that they are moveable/adjustable means they have the potential to give false accuracy over the length due to engineering flaws or even the introduction of foreign bodies or failure to tension the locking mechanism correctly. There are so many variables which makes them potentially unreliable but that is just my view and others may argue differently.
We all have differing views on such things but if I was making a shooting board from scratch now, then I'd use a precision square to mark out a slot on the top board on which the timber to be cut sits, into which I'd let in a suitable piece of hardwood for the stop block at a perfect right angle. If the shoulder is even just one degree out it's going to transfer to the wood being trimmed so a precision square is an essential as a starting point.
I'd also have quite a low stop block (maybe 1/2"-3/4" protruding) so that more weight can be applied from one's hand heel with fingers hooked around the stop or placed on top of the timber being trimmed. One of the problems with using a shooting board for short pieces of wood is the wood being trimmed is often able to rock so a low stop block is better for getting more weight/grip onto the piece to hold it steady which pushing the plane. If the stop block is too high it restricts the amount of pressure one can apply from their hands and results in inaccuracy.