That is to say: the asym crypto may strongly protect the precise (GPS or LTE triangulation) location from Apple and from others, but I do not see how a cloud-based system can ever hide coarse location from Apple and/or from governments as, given the short range of BT, they can reliably infer that a device (and hence its owner) is/was near whatever IP sends the encrypted precise location to their cloud. Then it's just a matter of mapping the device's "randomized" ID back to an actual user/phone. That seems easy enough as soon as a second device accesses it from an IP that's mappable to a specific residential address, Apple account, etc.
e.g.
A and B both log into iTunes or some other Apple service using a@apple.com and b@apple.com from HOMEIP at some point in the past. HOMEIP is never used by any other Apple accounts.
A(lice) and B(ob) exchange a secret and otherwise begin participating in this "private" tracking scheme.
A goes out shopping and while there it pushes its encrypted precise location to the Apple cloud, using random ID 424242, from MALLIP. Perhaps A's device sends it directly, or perhaps it's relayed from BT to Mall wifi to Cloud by C's device if A has both LTE and wifi disabled.
A few minutes later S(omeone) requests encrypted location for random ID 424242, from HOMEIP.
Apple (and any government compelling it to share information) can reliably infer that "Someone" was A or B attempting to track either B or A, and that the tracked phone was at/near the business address of MALLIP - their coarse location - even if they can't decrypt the precise location without the secret key. If you know from public records that A and B are married, and assume that women are more likely to be at a mall on their own than men, you may further assume that A is at the Mall while B is at home.
Result: the "private"/"encrypted" precise location beaconing has an unfixable metadata side channel that will leak coarse location data to Apple and to any governments that compell it.