My brokerage charges about $9 for stock and ETF trades. They charge $45 for mutual funds. What's so special about buying and selling mutual funds?
Mutual fund "trading" is different than stocks and ETFs, and thus the cost structure is different. Stocks and ETFs are traded on an exchange, where there are significant economies of scale, reducing transaction costs.
Mutual funds are bought from the fund company itself, which is a different mechanism and cost structure. Whether $45 is a lot for the actual work that is involved I have no idea, but my broker offers several no-load, no-transaction-fee funds.
So your broker is likely just making up for the costs of interacting with the mutual fund companies themselves.