We have two bags, for two different types of use.
One is the diaper bag. It's for day to day use and is always in the car. It's big, but really not all that heavy. It has everything we have needed in it, including but not limited to: numerous diapers, wipes (and lots of them), changing pad, butt paste, biohazard bags, antibacterial gel, feeding cover, bottle, water bottle, multiple changes of clothes, seasonal items (mittens, hat, sunscreen, etc), bibs, kids eating utensils, snacks, silicone placemat, small entertaining toys, sunscreen, ointments/medications as required.
Is it all necessary? Absolutely not. I too was skeptical about it at first. Turns out that its overkill in much the same way as the USAF arsenal is. The 'excess' of it has saved our asses countless times. The biggest problem I have with it is knowing which 'side pouch' my wife is directing me to for finding some specific item at her request. Sure any old big bag might be fine...But compartmentalizing really does help in organizing it all. Items designed specifically as diaper bags typically do this better than the more generic ones, as many are well thought out, but not that any large bag with lots of pocketing can't also be made to work acceptably.
The other is the 'dadper' bag. It's a single strap backpack for more outdoorsy specific event usage. It's small and carries only the bare necessities of 2-3 diapers, 3-5 poops worth of wipes, a biohazard bag or two, one minimal change of clothes, a changing pad, a seasonal item or two (mittens, hat, sunscreen, etc), a water bottle, and maybe a few snacks...Oh yeah, and my micro 4/3 camera that it was originally designed around and intended for. Its limited capacity does require inventorying it before every use though.
I will say that while a two-strap backpack may work fine when there is two of you, when the other can get things out of it on the fly, IMHO it will not be nearly as convenient or practical when you're on your own. You don't get to pick the time/location of needing to get into it, and it's not always going to be conducive to being able to put your kid down to get into the bag. Heck, even the smaller one strap backpack struggles in this regard at times.