I received a BeagleBone Blue about a month and a half ago, around the same time this thread was opened and I have run into the same issues. When using the on-board WiFi capabilities, the kernel panics and reverts to a read-only mode. This issue did not allow me to update or install packages (apt-get) on any OS distribution that I tried. I used both the pre-installed OS, a more updated Debian, as well as Ubuntu 18.04 and still ran into the same issue. Just like @me661 I tested different power supplies.
This happens when the WiFi is enabled and writing to the internal eMMC as well as the microSD card. I believe this to be a hardware issue, perhaps with the batch of BeagleBones that @me661 and I received. I am hoping to get a replacement BeagleBone Blue that does not have this issue or a refund on my order.
Below is a copy of part of the errors I got following an apt-get upgrade on the BeagleBone. No commands, not even dmesg worked afterwords, so this is the best I can seem to get in terms of displaying the issue. This error message is pretty long, so I can also provide more screenshots if this is too abbreviated (new users can only use 1 image per post in this forum). Thanks.