I find directional awareness lacking with muffs. If I'm spinning around trying to figure out where it came from I've already missed any opportunity and would probably be the looser in a close confines gunfight.
I've noticed the same thing no matter the type I wear. I can hear the sound and that does help, but I need to search for the source. I'd like to have my dogs hearing; she can hear a flea scratching on a squirrel at 200 yards, but mine? Too many loud noises in my lifetime before we knew the real danger.
It won't hurt anything to keep ear pro close by, but if you're doing HD "right" the last thing you would think about is that. You should be busy making sure the family is in the safe room (not to be confused with a panic room) behind your firearm. Calling 911 on speakerphone to report what's going on and your position in the house, priming the recording (and it will be recorded so be mindful of the words used) to help in your defense when the DA tries to decide if it was murder. Staying alert to keep the BGs away from the safe room or suffer the consequences of you shouting to them that you're armed and they need to leave. Yada, yada, yada. You'll be pretty busy. If a suppressor is an option that can be left on and no thought or time is required to protect all the ears in the house. But even w/o a suppressor a 9mm with a 16" barrel has time for the pressure to reduce before the pressure releases to the room*. A handgun not so much. Yet another reason I suggest to folks, when asked, to get a PCC for HD. Sometimes they even listen.
* It's Boyles Law. Double the volume of the pressurized gas and halve the pressure. A 16" barrel allows for 3-4 doublings of the volume. A 9mm operates at 35k psi give or take and the powder burns fast. Do the math. Here I assume max' pressure in 2"... 2"=35k, 4"=17.5k, 8"= 8.75k, 16"= 4.375k psi and that pressure is relatively nothing. Bottleneck cartridges are much worse; higher operating pressure most of the time and the first doubling happens quite a ways down the barrel.