There is no performance and technical reason going on here. This is 100% a Twitch policy thing, which likely only exists because of Apple's policies. If you're giving out a drop that can be used in an IOS app or game, you MUST enable a toggle that hides that drop in the Twitch IOS app.
The reason this policy likely spawns from Apple restrictions is because no such toggle exists for android devices. Apple, for some asinine reason, likely considers the app to app exchange of getting Warframe items from the Twitch app then using them in the Warframe app as circumventing their purchasing policies.
Also, very important. You are correct, it is only claiming the drop that is affected. You will still earn progress. The toggle hides the drop from the IOS Twitch app, but it does not stop the tracking. So you have to check somewhere else for your progress or to actually claim the item.