I have done everything you have asked: provided the model number, updated firmware, plugged it into the wall (not the USB) and I am still draining batteries every 2-3 weeks. Why?? My older Roku does not have this issue.
Roku has a problem and continues to "Thank" unhappy customers by saying they're passing the problem on. This has been going on since at least January (at least 10 months). Nothing concrete comes back except I see posts about plugging directly into power, which a lot of us undoubtedly do, or buying another remote. If Roku were an automobile manufacturer, there would possibly be a recall to either fix or replace these "battery eating" remotes. If these posts continue and nothing is done someone may decide to take "next steps". I like what Roku does but the trust factor is starting to tarnish.
I have the battery-drain problem, as well. I don't understand how powering the stick from a wall outlet could possibly have any effect on the remote's power draw. As others have done, I have been removing the batteries from the streaming stick remote after using it. The remote for my Premiere Roku last an extremely long time. Unlike that for the Stick, the Premiere remote does not have voice control. Could it be the remote with voice control is always listening, and that leads to a constant current draw? One of these days I should hook up my Fluke multimeter and measure it, but one would expect the Roku engineers already have the answer to that.