@stephenw10 it stops responding when manually disconnecting.
When I'm trying to send commands to the device it looks like the tty is frozen (impossible to type anything). I suppose the MPD script has the same issue thus throwing « CHAT: The modem is not responding to "AT" at ModemCmd: label. ».
If I'm power cycling the device it then appears as a new device (I suppose because the /dev/cuaU0.2 is still being used / locked).
Hence why I'm powering off the device before "cleaning" PPP and power it back on 3 seconds after ppp-linkdown is terminated. This makes sure the port is free and available for a new PPP session. But it really looks slapdash.