Well of course they do.
CAPS does a pretty good job putting an upper bound on the worst case result. They don't care if you screw your plane up because that's a known cost and you'll pay it back through premiums if you keep flying.
Dead sticking it has a very good chance of being no more expensive than a normal landing if you find a runway and not all that expensive if you find a good field or empty highway (i.e. a big towing bill) so of course most pilots would prefer to dead stick. But this comes with a small chance of you crashing into a daycare and maxing out your policy. The insurers do not want this.
Most decent pilots with good situational will be able to make the correct call between CAPs and dead sticking it. They're telling you to go CAPS all the time because they have to deal with idiot pilots too. It's the same reason every drivers ed program emphasizes brakes, brakes, brakes, despite the steering wheel being a far better way to avoid many problems. They don't trust you to make the call.
[citation needed]I know of a skydive place that does or at least used to regularly (like once or twice a week) dead stick it in a C182 because they would fly with the bare minimum of fuel (when you're flying up and down all day even a little extra weight costs a lot of money).
At least a non-pilot co-passenger might want to try their luck gliding to open area and then pulling it.
A fall of 10 feet puts you at ~17 mph when you hit. 20mph is a good approximation.
You’ll go wherever the wind pulls you. And might hit the side of something faster than 20mph before hitting the ground.
And hitting a crowd at 20mph.