It my not be a big deal for a completely solid state device but definitely pay attention to those notices for anything electromechanical, the issue isn’t the voltage but the current draw. And given that your broadband device is a transmitter, it could possibly matter at the margin…which for the topic under discussions could be precisely were you need it.

Can you elaborate on that? AFAIK the only real upside of the current draw properties of alkaline batteries are for very low draws where you'll get some additional runtime out of them. (e.g. I can swap the alkaline batteries in my tv remote every 5 years rather than charging the NiMH batteries every 2.5 years.)

If it cared about current draw would it still say not to use lithium D cells?

And I thought NiMH was better at current draw than alkaline.