When I was young, I could have handled sandals for all day walking, even pretty ones with heels. Nowadays, only athletic shoes and socks will do. My last couple of trips were with two (different) girls who wore Vans/Converse canvas sneakers. Comfy enough I am sure. After a couple of long days, they were the only ones in the group complaining of painful feet. Mind you, the rest of us had sore legs, etc but our feet in our athletic shoes were just fine.
At the end of the day - it's up to you and what works for your feet. I would probably have been just fine with canvas shoes/sandals when I was young (and never got caught in public in athletic shoes!). Definitely not anymore.
That said, I also find it depends on the speed and amount of walking. These days, I like to move relatively quickly and cover a lot of ground on Disney trips. I get excited and besides, I can always use a little more exercise to work off that Mickey bar. If I'm doing a slow, partial day and only in the parks for a few hours or know I won't be doing a massive amount of walking, my Crocs flip flops are just fine.
I totally agree with limiting the stuff you carry. I usually just carry a small crossbody purse to hold my phone (even better if I have pockets so I can skip this!). Last September I was there and bought a backpack. I had pretty much nothing in it (just my hat) and after a few hours, I was not a happy camper. It was definitely a lot more draining than just my little crossbody bag. It had to be the heat trapped on my back. Ugh.
Oh and the change of clothes if you go back for a break! I pack light and I have forgotten about this several times (planning only one outfit a day). In the summer heat, a shower and a change of clothes is WONDERFUL. I had planned to pack about 4 outfits and now I am going to bump that up to 6-7 outfits (I will be doing laundry every 3-4 days).