In all seriousness, I appreciate the effort you went into for researching this. It can be a pain.
I think it would have been better without the passive aggressive comments like "evidence you demand" and "that would be lame".... but okay...
There are a number of issues.
1) In everything you have shown, at no point has anyone made any claims of a slinger actually using only one hand to load the sling. That is not necessarily a deal breaker, but it *is* an important distinction. No matter if you think its 'lame' to point it out.
2) I have never said it was physically impossible to use a sling while holding a shield. Of course it is. I can do a whole lot of things while holding a shield. But there are 3 things to consider...
A) Can you use the sling with the same speed and accuracy with and without the shield
B) Can you actually use the shield to protect yourself while you are also using the shield hand to help load.
C) Does allowing the shield hand to also help load break any of the rules of the game.
A) One of the people you presented has
another video where he is slinging for speed, and it take more than twice as long to sling with the shield as without. And that is not even considering having to also use the shield for defense. (which is likely to slow you down even more)
B) Both of the videos you presented make it obvious that the shield is *not* going to be very effective at defending. Either the shield is out of position, or the slinger is looking in the wrong direction (down usually), or the shield hand is occupied helping load and can't move well.
The picture series author seems to indicate that he could keep the shield on target, but anytime the hand is busy loading, it becomes problematic to also block. And as mentioned, anytime you are blocking, it will likely slow down the slinging even more.
C) I guarantee I can create a video where I am using a shield and using a spear, or a greatsword, or a crossbow, or a polearm. I even think if I use the right shield, I could use a bow. But the rules of the game dictate that when a hand is being used for something, it is not free to be used for other things. Now DMs get to adjudicate, and if using the shield hand was for something trivial (like holding a javelin, or holding your sword) I could see it. But from a DnD rules perspective, you are trying to get one hand to do two things, and the rules tend to frown on that.
As for the pictures... *of course* slingers used shields.... *especially* in a seige situation (which both pictures are). They will gladly give up their offensive ability to get much better defense. But you are asserting that they can get that added defense with *no* change to their offense....
So yes, you can use a sling while holding a shield, except
You will sling much more slowly
Your shield will not work as well
you will be changing the rules of the game.