I'm an installation contractor for cox cable in Tulsa. I can't say for sure about phone company policy. Normally on an install if it does not have a wire from the pole to the house we install one at no charge for new customers.
I install cox phone and I CANNOT touch or remove any Bell, AT-T, or any other company's box or aerial. Actually I believe once it is attached to your house you "own" it.
So to answer your question.....
Why?
they just want to make it harder to switch back if you decide not to stay with them (possibly against the law for them to remove stuff)
Is there any technical reason for this?
no reason at all, they should install their own box and remove your house wiring from the old box and swing them over to the new one
Can I refuse to let them remove the junction box and wire?
yes