I think this is actually a common frustration for a lot of people visiting any of the parks. And while I often wonder why so many bring so much, and it is far more becoming the rule than the exception, it is something Disney needs to address immediately.
Imo at the very least ALL stroller traffic entering the park, any park, should be designated to one side or another for inspection.
A line for no bags is already in place.
Back packs line and a small bag/ purse line. This would alleviate frustration. You read a large sign, you follow it. Simple enough.
Now, I'm a parent. Ive been traveling with my kids from very early on. I have never had or needed the amount of "stuff" for two kids and two parents that I see at WDW. When they were small, and in strollers, we brought the smallest most convienient least obtrusive one. I would have never brought a jogging stroller to WDW. They are too big, invasive of space and take up half a bus traveling between resorts and parks. I used mine for... jogging. Only jogging. Because it's a jogging stroller. Sometimes you have to think about not just yourself when traveling, but generally those around you.
So, if one must hit the parks with two jogging strollers a large full cooler, three backpacks, two duffle bags, two diaper bags, a fanny pack for everyone, a purse, six blankets, four butt cushions for curb sitting, and leashes for the kids, be prepared BEFORE you get to the tables. Everything open, ready to go. Take into account those around you. Understand their frustrations as you'd expect them to understand why you have to have all you brought. This is a two way street. It's not couth to have this "suck it up and deal with my load of stuff" attitude, and then not be ok with "well, damn, why do they have all this stuff, and aren't prepared in line, taking forever" attitude.
And when boarding the buses, it's cool to go ahead and take you kids out of the stroller fold it up and be ready to board BEFORE the bus is loading.