First, let's not act like Bloomberg is any stranger to the various types of criminal profiling out there. Second, let's not pretend the practices aren't effective (right vs. wrong is where the debate is).
So, essentially, Bloomer is conceding the fact that his pet civil rights abuses haven't worked because they haven't been focused on those most associated with the societal ill. Honestly? That's a good thing; it implies he would be less hostile toward proposals from our side that rescind his admittedly ineffective tactics against the vast swath of the population that is needlessly effected by the policies (I'm sure the 'needlessly effected' part is something he'd deny, but if he truly realizes the pointless nature of these tactics, he won't fight hard for them, either)
So, he'd possibly be comfortable with doing away with blanket policy so long as 'something is still done for the children,' albeit on a more focused scale. It would seem AWBs, safe storage laws, and possibly even BGC's would fall squarely in this area of "needlessly broad and of limited effectiveness/deterrent."
At that point, we'd basically be back in the good 'ol Jim Crow days, wherein gun laws were only enforced in minority/poor ghettos (and by extension, almost universally against the minority/poor persons at large). Not exactly a glorious development, but --from a strictly Machiavellian/tactical point of view-- you end up with fewer law abiding Americans subject to terrible laws and civil rights violations (keep in mind; those in ghettos are already infringed with the present state of affairs). You could call it a sort of improvement, beating back the progress gun control has made from the Jim Crow days to now ensnare all Americans, rather than those who happen to be unfavored.
From that vantage, with increased numbers on our side (owing to reduced gun control in outlying areas where the money/low crime resides) it would be much easier to then roll back whatever gun control schemes are enforced against serfs in the feudal domains. For this simple logical progression alone, I don't think Bloomberg actually means what he actually said. He would probably clarify it as all further infringements needing to be structured so as to disproportionately affect* those most likely to commit/be victims of crime**.
I think it would be interesting to engage Mr. Bloomberg from his own perspective; "of course we should structure our preventative crime laws*** to have the most impact and implications for those committing the bulk of the problem, which is why we should rethink existing schemes like 'universal' background checks and blanket prohibitions on equipment." His argument has a very straight forward corollary, but it would be entertaining to see him deny it (and thus refute his own arguments on targeted enforcement/statute)
*Somehow I doubt such language would survive 14th amendment scrutiny, but I wouldn't put it past lawmakers to try (though I'm sure they'd use all sorts of Orwellian doublespeak to get around it)
**Underpinning the anti/statist belief system is the notion that criminality is a "two to tango" situation where the presence of both victims and predators are the problem, so both must always be addressed simultaneously
*** <shudder>