All reasonable players understand that you don't want anyone to be able to log on to the same account from two different devices. Having said that, being required to input ID & password every time you switch devices is completely unnecessary

There are three other solutions that are much less intrusive and just as effective.
1) If you log on to a second device, it could pop up a message informing the player that they are already logged on from a different device.
2) If someone logs on from a second device, automatically log them off of the first device.
3) A combination of 1 & 2 - a pop up message informing that they are already logged on from a different device, and asking them if they want to be logged out of the first device and on to the second.