Not necessarily. It only leads there if the flow has to be zero - reducing the flow and/or making black market guns more expensive than alternatives would still be worth doing (it would have a significant effect on armed crime long before the number of available black market guns reached zero), and could be achieved through some degree of owner responsibility (e.g. requiring guns be in a safe, have trigger locks, be kept separately from ammunition, limit the volume of ammunition stored at home). Better still, that doesn’t even have to require legislation!

Some of those steps would also most likely reduce the number of unpremeditated killings, e.g the freak accidents where babies shoot parents with the gun in their mother’s bag, kids shoot each other with a gun taken from a nightstand etc.

Of course, the usual response to this is some variation on a theme of the fear of crime, to which the only response is that violent crime has been declining for years and the people making most noise about it are frequently invested in the weapons industry.