Are you saying that the 8V minimum specification already accounts for being given less than 8V? If so, I think that's a very unwise assumption to the point that it's plain wrong to assume.
Come on! I say that the 8V allows for the room the regulator needs to provide the internal voltages, and 8V or above is an OK supply voltage, so 9V certainly is.
If the regulator design says 8V minimum input, it's 8V minimum and not guaranteed or even likely to function properly below that.
It is not the regulator design that says 8V minimum input, it is the device specification sheet that says. So the "I would provide a bit more than the regulator minimum" already has been covered by MikroTik.