Transaction fees in the Bitcoin network are determined per transaction and are paid by the individual signing the transaction, not based on the size of the UTXO set. Miners give precedence to transactions based on their fee rate, which is calculated in satoshis per (virtual) byte, allowing them to maximize their profits from the fees collected.

Utreexo is a protocol that aims to minimize the size of the UTXO set, which could lead to questioning the relevance of discounts related to the UTXO set size. Since the transaction fees are not levied based on the UTXO set size but rather on the transaction itself, any discount tied directly to the UTXO set size might seem unnecessary and could potentially introduce inefficiencies into the system.

Nodes operate independently within the network, sustaining themselves without direct financial support from the transaction fees generated. Therefore, the operational costs of nodes and the expenses borne by node operators are separate from the dynamics of Bitcoin fees. In this light, the impact of Utreexo on transaction fees would be indirect, as its primary function is not to influence fee structures but to streamline the handling of the UTXO set.

In essence, the introduction of Utreexo is expected to enhance the efficiency of the network by compressing the UTXO set, but this is independent of the Bitcoin fee strategy, which remains focused on transaction attributes rather than the state of the UTXO set.