You're not adding an intermediary. The broker and the exchange do different jobs. Coinbase is an exchange and a brokerage firm. Under the current arrangement, Coinbase is providing its customers with both exchange and brokerage services, so Coinbase customers are paying for both. If Coinbase was providing exchange services to brokerage firms, and these brokerage firms were providing brokerage services to retail investors, these investors would still be paying for both services (directly or indirectly), but prices would be lower due to competition among brokerage firms.
I don't understand what you mean here. In what way do you consider Coinbase a brokerage? Users on Coinbase can trade directly on its exchange and pay trading fees. Restricting the exchange to only brokers would mean that the middlemen ("brokers") would now pay the trading fees and pass that cost onto their customers, plus some brokerage fee (which means a higher total fee for users). The broker-intermediated trades are necessarily more costly than the direct trades.
- custody of assets
- margin trading
- customer support
If the answer is yes, then Coinbase is providing typical brokerage services which could be provided instead by firms independent from the exchange. Do you not agree?
You're not adding an intermediary. The broker and the exchange do different jobs. Coinbase is an exchange and a brokerage firm. Under the current arrangement, Coinbase is providing its customers with both exchange and brokerage services, so Coinbase customers are paying for both. If Coinbase was providing exchange services to brokerage firms, and these brokerage firms were providing brokerage services to retail investors, these investors would still be paying for both services (directly or indirectly), but prices would be lower due to competition among brokerage firms.