Parents with children are (or should be) the universally agreed exception to the back pack / carry-on rule. Most people are understanding of that situation. We are past that stage now, but back in the 90's we were travelling back and forth to the USA on a six week rotation with an 18 month old and a 3 year old. If we were going to the east coast, it might be 30+ hours of travel with connections here and in the US. My wife got very good at packing. We even took car seats we had bought back and forth as the fitting were different in the US. We had this ugly squarish Puma backpack that could fit an amazing amount of stuff (nappies, spare clothes, soft toys, books etc.). It was within the carry-on limits (just).
Nowadays I still travel with a backpack, just a smaller one. As others have said, I carry it on/off using the top handle. My aim is to get out of the aisle and seated as soon as possible. As soon as I get to my seat, the backpack goes in the overhead locker on it's side to minimise space taken, with the intention that it stays there untouched until I get off if possible. I get organised before boarding (you have a lot of time waiting at the gate/lounge, so you might as well do something). If possible I wear a shirt with two pockets to hold phone, headphones and adaptor, boarding passes, passports etc. For a short flight, shirt pockets are usually sufficient. Depending on the flight length, I then have my fall-back strategy. For medium length flights I have a small zip up cube, like a packing cube but with a nylon material covering rather than mesh (got them from Ikea years ago - small cubes were intended for toiletries, larger ones for shoes I think). In this goes anything else that is needed (Kobo or other reading material, reading glasses so I can see the IFE screen without craning my neck back to watch the movie through the bottom quarter of my multi-focals, water bottle etc.). I carry the cube on in my other hand or quickly get it out of the top of the backpack. It can be stowed the under the seat, in the seat pocket, or just held in your hands for takeoff/landing. For long flights I have a medium sized cube for all of the above plus a jacket for the cold (a cycling jacket that is small, lightweight and can be scrunched up) and even a neck pillow. It can be stowed under the seat without restricting the space there.
but it would help a bit.
