I have seen various videos on YouTube of people making freehand crosscuts with a table saw.
Freehand cuts on the table saw are a bad idea, and I wanted to demonstrate just how dangerous it is. So I set out to do an experiment. I hung a cloth behind the saw to catch whatever would get thrown from the saw and then held the piece from the side so I would be out of harm's way.
Surprisingly, it took me quite a few tries before I was able to get my saw to kick back, and even then, it was just enough kickback to throw the piece off the saw. Nothing violent.
I tried again, with another piece of wood. This time I was able to get enough kickback to throw it well clear of the saw, though it hit the floor at most 1.5 meters away. So the workpiece wasn't flying fast enough to cause injury.
This reminded me of when I tried to demonstrate sleeves getting caught in a table saw in a way that was realistic. I was unsuccessful, and people read that as "Matthias says it's ok to wear long sleeves on the table saw". So those same people will probably read this one as "Matthias claims freehand crosscuts are ok". Over the years, I have learned that proponents of safety, security, and religion are often impervious to reason :).
Kickback is almost always caused when the workpiece can rotate and so will pinch the blade. If the blade, pushing on the workpiece, causes it to rotate further, that can further pinch the blade, causing the workpiece to be thrown off the saw.
For example, any workpiece that is wider than it is long against the fence can end up rotating a bit. The blade then pulls the piece further, causing it to rack between the fence and the blade, forcing it more and more rapidly into the blade, resulting in kickback.
The bigger risk with kickback, I think, is that your reflex may be to try to grab the wood and get your fingers in the blade. But even reflexes are a function of what you think. Most people, if they trip while holding something precious will fall in a way to protect that thing, but drop it readily if it's not valuable. So I think it's important to be just a little frightened of the blade. If you are scared of it, your reflex won't be to reach for it.
To prevent kickback from crosscuts, you should always use something to help guide the workpiece, such as a miter gauge or a table saw sled. Your cuts will also be cleaner and more accurate.
And just a note, I have seen the video "Kickbck caught on camera" so you don't need to send me a link to it (I say this because people I get sent links to that video qutie frequently). This article is about kickback from freehand crosscuts.