If iPhone Mirroring simply won't cooperate, the free method that fits your "no AirPlay" preference is QuickTime Player using a USB cable. To mirror iPhone screen to mac, it's built into macOS, requires no third-party apps, and works reliably:
The steps for mirroring iPhone screen to Mac:
Steps 1: Connect your iPhone to your Mac with a Lightning cable.
Steps 2: Open QuickTime Player.
Steps 3: Go to File > New Movie Recording.
Steps 4: Click the dropdown arrow next to the record button and select your iPhone under Camera.
Your iPhone screen will appear in the QuickTime window instantly. This method also lets you record the screen if needed