For the most part, I agree with what you posted as a response. I'm all for keeping firearms out of the hands of persons who should not have them.
We have background checks for all firearms purchases through a licensed dealer and we require the same for private transfers. However, there is no way, short of a gun registry, which I oppose, to enforce the latter. Also, the databases with which our NICS and state police operate are woefully inadequate.
By what means would you enforce any law that require that guns not in actual use or being maintained, be locked up? Child access prevention laws might prevent some incidents but it's essentially reactive; enforced only after a mishap, unless there is a provision for periodic inspections of compliance. That might be a Fourth Amendment infraction.
I know enough about gun control progressives to know they'd gut the Second Amendment. Just look at some of the posts here. Example: You need to join a militia in order to keep and bear arms.