Good Answer already from @SaSSafraS1232 but I wanted to address some additional points you raised.
If anything, a kickback on a router should be more catasfrophic as the tool can be thrown from your hand and take a nice bite off your navel.
Compared to routing a length of wood a router will generally have greater mass. And with routers where there's a notable risk of a dangerous kick (i.e. powerful enough) you have two hands on it, gripping handles specifically intended for controlling its movement.
So together, if thrown the router will tend to go less far, less quickly, compared to a piece of wood snatched from your grip.
Do a mime of how you would typically feed wood past the bit in a router table.... see how not under control the wood is compared to a router being gripped and controlled with care and attention? Also notice that one or both of your hands is near the level of the spinning bit, rather than much more safely positioned up on the handles of the router itself.
This is of course especially hazardous as most router tables don't have a safety guard (as they should)!
In the same articles, climb cutting usung a hand held router is not as dangerous and even encouraged to get a good edge.
I think it should be highlighted that climb-cutting is not the only way to get a really good edge.
IMO it's also something you shouldn't do without a full understanding of the motions involved and the potential risk, so if in doubt don't do it.
There are other ways to ensure a superior cut surface, none of which involve increased risk to the user, or to the workpiece, (e.g. clean, sharp bit and taking a final 'skimming' pass to remove a very small amount of wood).