I bought two Nook STs last month. Both came with a wall charger. I have no idea why you are saying it doesn't come with one?
I had trouble with high battery discharge (~20% day) with the first unit because I used a trick to skip the OoBE so I didn't have to register the device. Since I couldn't work around the battery consumption, I reinitialize the device and created a B&N account without a CC from within the Nook ST and completed the device registration. It worked fine after that.
With the 2nd Nook ST I just registered it using the same account as the first device. I've also had no problems with that device either, although right now it's shutdown completely as I'm reading a hardcover.
Both devices have the wireless shutdown and are always charged with a wall-wart, either the B&N one or another generic one. The first one was gifted and I recommended charging it about every two weeks. From the limited time I ran it, 3 weeks of normal use should not be a problem either.