On rides like Mummy, we regularly ride with lanyards, and never had anyone question those. How else would you take advantage of the express pass line? On those rides, you don't have to empty your pockets, they mostly just care about bags.
For the few rides like Hulk, with metal detectors, then you kind of have no choice, unless someone in your group doesn't want to ride, and will hold everything or you want to take turns riding (but that wouldn't really be a better solution).
We do use the lockers, but I'm going to say it is a bit of a pain. Individually, it doesn't usually take THAT long to get your stuff, but collectively over the course of the day that time adds up. If you are able to go without a bag, that is easier. While I've only had problems with malfunctioning lockers a few times, it has happened. It also sometimes happens that you get stuck behind someone who forgot their locker number. To be fair, the lockers aren't all exactly the same. Sometimes you have to enter your number, but other times you don't. (unless there's a problem) I can see how that could be confusing, especially after you use multiple lockers all with different numbers.
If we stay onsite, esp the deluxe hotels, then we often only carry a bag only part of the day.
One more thought, I haven't done this per say, but I once saw a family who wore tiny pouches tucked into their shirts.