is MDIO required for PHY?
By definition, "strapping option" is a configuration that is set in hardware by pulling up, down, or no pull on certain pins, which usually takes an effect only at release of hardware reset. This is done to save the number of package pins, which saves on costs. Therefore, there is usually no need to waste GPIO pins on that, unless you plan to do something totally crazy with communication channel.

The operations that are "required" requires you to select certain mode of operation (see Table 3-4 of datasheet), hardwire the straps accordingly, and stick to it. If you want some super-flexibility, you will need to control all straps and hardware reset pin to the PHY.