I'm not a LEO but I know a few - I don't see the local police giving up that kind of autonomy. I'm not saying it couldn't happen, just not in the current environment. Providing all this US Military surplus could be a way of 'getting them onboard'. The relationship between the State NG and US Military comes to mind - it solved some of the problems perceived during the Spanish American war. I've seen the rivalry's built up between those with Fed Cred vs local LEO's. It gets nasty at times. I think it would require a paradigm shift that could take a year or so. The local leadership would have to be replaced. A lot of LEOs are rather passionate about their responsibilities and protecting their communities - they just don't get as much media time.
I think they (DOJ) may continue with what they do now - the Feds move in to an incident and take over with their own (deputized & out of normal jurisdiction) help. This happened in Ferguson with the State Police taking over - they brought in help from other communities. Why create a national police force if you can walk in and take over where ever you want to. You don't need to attend the tedious details of day to day administrivia & emotional baggage.
From a psychological pov for the Feds, it gives you an out, you come into a screwed up situation wearing the white hat - the daily friction of a national police force would be an unnecessary lightning rod. Let the local enforcement structure soak up the anger and show how the Feds can come in and make it "better" (along with the media, of course). It seems to me that this is too valuable a propaganda tool to discard at the moment.
my 2ยข worth.
if a national police force does replace normal local law enforcement
I'm not sure how that would work - not my area of expertise.