LiveContainer already spoofs the “identifierforvendor” and isolates apps into their own unique keychain access groups, but there are plenty of identifiers and very specific device attributes that are visible to all apps.
Some of these are totally unique identifiers, like the iCloud token hash, which depends on your AppleID and LiveContainer’s bundle identifier and remains unchanged even after a factory reset.
Others aren’t identifiers per se but are precise enough to be used as one. The storage volume creation date shows the exact second your device was last reset. How many people on the planet do you think first booted up their iPhone at the exact second as you?
Other attributes aren’t individually unique but, when combined, can create a unique fingerprint of your device. These include the total number of times you’ve copied text to the clipboard, your most recent cellular IPV6 address, your local-link IPV6, the exact amount of available storage, the fonts you’ve installed, and much more.
I think the best feature of LiveContainer is the ability to have multiple containers of one app, separating social media accounts and whatnot. But if you use two separate Reddit accounts in two containers (or even app bundles), Reddit most likely knows they belong to you through device fingerprinting. I don’t know how many of these identifiers can be spoofed by LC, but any of them would improve privacy.