Firstly, miners do not technically intermediate transactions. Transactions are fixed and sealed by the parties involved and can't be modified. Transferred funds are never in a possession of a miner, not even briefly. Miner can't take them, can't redirect them, can't change the amount, etc.
Secondly, it's not a specific miner that confirms the transaction. It is the ever-growing group of miners. Transaction finality is ever only probabilistic. If you think picking by law the "first" miner then this is completely arbitrary and 1-block chain tips are routinely orphaned in all cryptocurrencies.
Finally, many persons and businesses accept unconfirmed (not mined) transactions, for relatively low-risk goods and services.
If you really want to regulate miners (which is making a crime running certain algorithms on your personal computer - a terrible idea), then at least please come up with a new name and new framework, because "money transmitter" or "financial intermediary" is simply incorrect.