Actually I think a number of people on the gun-control side want exactly that. Here’s a recent admission posted on this very forum just yesterday.
It seems pretty clear to me that they know they can’t get what they want now so they are going for a little at a time. I think the preferred term for that is incrementalism, and I do think incrementalism is their best shot towards their ultimate goal. A number of gun rights advocates know this and that’s why they oppose it.
Also if you look up the proposals of the 1994 assault weapon ban, you will see that some shotguns, very suitable for home defense, were in fact banned. I forget though, did that have a measurable effect on crime?