I do believe the Courts, not the CON crap 'dear leaders', have held citizens are allowed firearms in such defense.(Heller and McDonald, you must have heard of them being a lawyer and all)
If you refer to the types of weapons and ammunition capacity of said weapons again NO Court has upheld that 'theory' I am aware of.
The biggest problem with your attempt to equate the 'self defense' function for LEO and citizens is the duty side. Cops are not 'other citizens' but COMMISSIONED Law Enforcement Officers. Cops don't just walk around and only use deadly force if a mugger demands their wallet. Nor is the biggest likelihood of confrontation while asleep at home because of a burglar. LEO is far more likely to confront an armed biker gang than a one way range warrior having a fantasy run on some COF.
I find it interesting so many who claim Commissioned Law Enforcement is the same as 'other citizens' rarely, if ever, volunteer to go through the Reserve Academy and work as a Reserve Officer, since it is the 'same thing' as just going about your business as a 'other citizen'....