The reason it is not good to power your multimeter from mains power is because now (I believe) the negative terminal on your meter becomes Earth ground, or at least Earth ground referenced, and depending on where you place it in your circuit, you can easily cause something to blow up or get damaged or hurt yourself. Such meters need to remain "floating" in terms of their power supply, which is why they are battery powered.
Also, the resistance you calculated would lower the voltage to the 9V you want only at the current you used to calculate; the current draw will certainly vary and cause that voltage to fluctuate. Also in general, this is not how voltage regulation is done at all.