Since running local nodes is almost impossible on mobile devices
I actually think that in the not too far future this will stop being true!
The two key technologies are (i) block-level access lists, and (ii) ZK-EVMs. With these two things, a node will be able to have full confidence in the correctness of the chain, and track state updates, without needing to do any local EVM computation, and without needing to store any auxiliary data (eg. intermediate tree nodes) other than the state itself. That means that even today you would be able to have a minimal fully state-tracking node in under 100 GB (!!)
Once the state increases further, you can do partial-state nodes. The great majority of Ethereum’s state is garbage, and so we could find ways to filter it out. Alternatively, there is a decade-old trick from Bitcoin land: design the wallet so it only issues addresses that start with some hex character (eg. 0x5...), so you trade off between a smaller anonymity set and only needing to track 1/16 of the state. The other benefit of this design is that you get reduced bandwidth reqs because you only need to download part of the BAL (if the BAL is designed correctly: in sorted order by address)
So we have two promising paths toward better privacy of reads. And they are combinable! Eg. a partial state node for the 4 GB of state you are most likely to access + eat the inefficiencies of PIR for everything else