The dado jig I built will hold a piece of material up to twenty-four inches wide, so it, by itself, is big enough to stabilize a router operation, since it is clamped to the wood. I’d have no qualms about using my 3hp Porter Cable on it (other than it would be over kill and the thing weighs as much as a small VW).
The most common use for this would be to, for example, router a shelf three feet or more feet tall. I’ve used it several times and never noticed any inclination to wander in response to the bit. That said, I always use my 1-3/4 hp and I’m only going down about 3/8" or less at a time.
When I route, I usually have one hand laying on the table and the other pushing and pulling the router (I use a D handle for this). If it were inclined to move, it would be no more complicated to keep the jig still than to control the router, of course.