Put aside personal objections and think about a power grab from state and local authorities.
I think all this EO does is prohibit the federal government from providing certain military equipment to state and local government agencies. I suspect that is within his power. If your city or county wished to contract with suppliers of military hardware to purchase same with their own taxpayer-provided funding, and Obama tried to prevent the sale, that then might be a different matter. He'd probably try anyway, of course.
Consider the fact that no military equipment was used in the racially exploited deaths.
Obama puts stricter controls on military-style for police
With scrutiny on police only increasing in the ensuing months after a series of highly publicized deaths of black suspects nationwide, Obama also is unveiling the final report of a task force he created to help build confidence between police and minority communities in particular.
The federal government also is exploring ways to recall prohibited equipment already distributed.