Since UTXOs are required to spend funds, where does Trezor get the unspent outputs from?

• Storing them in the hardware requires you to plug it in from time to time to update the UTXO set. You could even run out of UTXOs!
• Host-side blockchain scanning for UTXOs from a given deterministic wallet is very expensive (if not impossible since there are infinite addresses in a deterministic wallet).
• You can't build a "wallet -> UTXO" index for the same reasons above.

What am I missing?