How much shooting in close quarters have you done with a 556 or otherwise?
I can assure you all of its deafening (from a guy that has shot tens of thousands of rounds from inside vehicles, inside houses, inside other confined areas, and been on more FISHing expeditions than I can count (Fighting In Someones House)..
I can also assure you than when fighting for your life.. the last thing on earth you are concerned about is the noise..
While I dont know the laws/rules in Canada regarding suppressors.. They are becoming more and more prevalent here in the US.. and a short, affordable 6" can on the end of a 556 carbine solves the noise problem, if it in fact is a deal breaker for someone.. Combine that 6" can with a bullpup like the Tavor, or a SBR.. and you have a weapon that is just as easy to work in a close quarters situation as a pistol caliber carbine or an SMG.. and FAR easier to manipulate and work than an 18" barreld "combat" shotgun.. while also bringing SIGNIFICANTLY more ammo on the platform to the fight than the shotgun, and SIGNIFICANTLY more terminal performance than the PCC..
Again.. there is a reason FBI HRT, SEAL Team 6 / DEVGRU, Delta/CAG, every major metropolitan SWAT team in the US, and every western international counter terrorist team ditched pistol caliber platforms by the early 2000's (the trend started in the 1980s).. and have resorted to only using shotguns for breaching (that also started in the 80's and was pretty much complete by the early 2000's)..
Simply put.. Joe Biden got it wrong.. if you want to defend your home.. a shotgun is one of the worst possible options.. and a pistol caliber carbine isnt much better..
A shotgun with lethal ammunition (buck or slugs) has serious over penetration issues, isnt an inherently accurate weapon suystem (its pretty much a given that in a CQB situation there are going to be other friendlies in the area), lacks a precision shot capability, has limited ammunition on the platform, and is slow to reload..
Pistol rounds depending on circumstances and medium often significantly over penetrate in CQB situations where 556 does not.. and lack the down range ballistic "kill" capacity of even a small caliber centerfire rifle (like 556)..
A PCC or a shotgun... or even a bowie knife.. is certainly better than nothing.. If a PCC or a shotgun is what you have... then by all means use it.. The most important weapons anyone brings to a fight is their brain and their mindset..
But dont kid yourself into believing bullshit like a PCC or shotgun is superior in any way, shape, or form to a centerfire rifle in anything other than very specific and limited scenarios...
If the opposite were true.. why do organizations that can literally choose any weapon system on the planet they want, not still conduct CQB with shotguns and pistol caliber weapon systems? And havent done it in 20 years...
All the above said.. I LOVE the HK MP5.. I conducted hundreds of raids with one years ago.. trained heavily with it.. and think it is the quintessential SMG.. Accurate, reliable, easy to shoot, etc... I also carried a Rem 870 and a Benelli M2 professionally for a while...
But, like everyone else.. the minute a reliable centerfire rifle caliber option became available.. I dumped the MP5 and shotgun and never looked back..
It is simply that much better in every measurable and meaningful way.. if you are talking having the sad misfortune of needing to shoot people at CQB distances..