They have package pick up just like Disney does. Shop around, have the packages sent to the pick up location and get it on your way out (we've done this before). And just like Disney you can have your packages sent to your on-site hotel (this I haven't done because we haven't stayed on site before).
I give Universal credit though they don't want injuries on their rides like what happened at Dueling Dragons.
Sometimes when I see how much people bring to WDW and onto rides and the at times delay getting in and out of rides in order to stash their bags I become grateful for Universal's process on some of their rides.
At our local amusement park this is the following rule regarding loose articles: "purses, backpacks, beverage containers or any other loose articles may not be taken on most rides.These items may be left in a locker, your vehicle, with a non-rider, or at the owner's risk on the ride platform" In order to have loose articles the following is advised: "To secure loose articles, a cargo pocket must fasten with a velcro or button flap or a zipper, a waist pack should fasten around the waist and have a zipper closure, and a jacket pocket must have a zipper closure." Along with this advice "we suggest that you bring into the park only items that can be safely secured in cargo pockets, a waist pack or a zipping jacket pocket." So I guess YMMV on not requiring stuff. Granted Universal is just more restrictive in that they would rather you just not have anything loose period but they aren't the only ones to have stock in large bags on rides and rules regarding securing loose articles.
*Sorry not trying to go off on a tangent too much here.