I described an alternative way for SPV wallets to learn about fees some
time ago. It requires a new transaction version that embeds output values
into the signed data. Then an upgrade to the P2P protocol to send UTXO data
along with transactions when they are relayed.

The idea is that the wallet sets a Bloom filter with an FP rate that
ensures it will see some random subset of all transactions being broadcast
on the network, and with the extra data, it can calculate the fee paid.
Once a transaction broadcast is observed the wallet includes that tx hash
in its next Bloom filter, thus it can see which block the tx confirmed in.
By measuring the amount of time that passed between a broadcast and it
appearing in a block, it can calculate its own tables of fee paid:time
taken.

This has the advantage that you don't have to trust miners to publish data
accurately. However it requires some protocol upgrades and of course, a lot
of new code in SPV wallets.

The way Bitcoin Wallet for Android handles fees currently is to just update
a hard coded value every so often.