I think the main point you're missing is that there are three categories related to what is permitted on when it comes to attractions:
1 - There are attractions where any bag type is permitted, which would include fanny packs, backpacks, shoulder bags, etc. Neck fans would likely be permitted to stay on you for these rides as well. Off the top of my head, this includes rides like the Simpsons, Spiderman, Transformers, Hogwarts Express, Seuss rides, Jurassic Park, etc.
2 - There are attractions that have free locker banks adjacent to them where they limit what is permitted on the ride. These are rides with more robust safety restraints and are a little higher intensity, so they limit what can be carried on so that nothing becomes a projectile, nothing gets lost, and so that nothing interferes with safety restraints. On these rides, most TMs will permit fanny packs with three prong clasps on the ride without having to store it in a locker. As with anything, its all up to TM discretion so I would not say its 100% permitted all the time but as a general rule of thumb, this is what seems to be allowable. You can also put any items in your pockets that will fit. Anything that doesn't fit in your pockets or fanny pack would have to be stored outside the ride in a free locker (i.e. neck fan). This includes rides like Forbidden Journey, Gringott's, Mummy, Men in Black, etc.
3 - There are currently two attractions (Hulk and Rip Ride Rockit) that have metal detectors at the queue entrances. These rides do not permit *anything* on your person except for a lanyard. All bags and loose articles, including fanny packs, fans, cell phones, etc., have to be stored in the free adjacent lockers. I assume Velocicoaster when it opens may require the same, but I think that is still TBD.
I believe most if not all of the lockers at this point use your ticket to scan and unlock your locker, so you'll want to keep that on you in some fashion. This is why so many choose to wear lanyards. Its also worth nothing that most (all?) of the free lockers are quite small, so a backpack likely would not fit in them unless you have a drawstring style that is half empty and can be squished down. There are larger lockers for cost at the front of the park that you can rent for a day or half day. If you think you need something larger than a fanny pack or crossbody style purse to carry everything, I'd suggest renting a locker at the front of the park for the day - I think its something like $10 for the day? You could even bring a fanny pack in addition to that if you want to keep something on you too while walking around.
