To be fair, there is zero ability (outside of undocumented and forbidden private APIs) for an iOS app to even request access to browsing history, bookmarks, or app history.
Actually that's backwards. Android moved to the new permission system (fewer perm groups, runtime user permission) to be more like iOS. It used to be that all permissions were granted at install time, which made apps much more likely to ask for onerous permissions because the user is unlikely to read the list or turn back.
It's likely they don't try this on iOS because iOS simply doesn't have the APIs to do this under any permission. It's a philosophical platform difference about what the user should be able to allow apps to do.
Uber doesn't try to pull anything like this on iOS.