This is very popular in Seattle. The biggest road racing group here, Orca Running, has switched to cupless running under the guise of saving the environment. They're still happy to hand out gaudy medals and T-shirts, and they distribute bottled water at the finish. If they were really serious about the environment, they'd use compostable or reusable cups at the aid stations.
Orca Running only does races up to half marathon. I don't care about drinks for a 5K or 10K, but it's a serious problem for half marathons, and they operate a huge percentage of half marathons in this area. They took over the fastest half in the area (Lake Sammamish Half), and it's now cupless.
Aid stations are now unmanned or have one or two people. I'm sure it saves them money and effort.
I'm old and not particularly fast, so my race pace for a half marathon is about 8:00 mpm. I ran the Lake Sammamish half, no cups, chasing a PR. Filling the cup is actually quite quick and carrying the cup is NBD, but coming to a screeching half every 2 miles to get a drink is incredibly demoralizing. Even at 8:00 pace, it's really hard coming to a complete stop every couple miles.
OP - I don't know what to recommend. I have tried a variety of hydration packs and they all suck, plus the weight will slow you down. But stopping sucks, too. The only real solution is to vote with your wallet and not run cupless races.