I'm sorry about the trouble you guys are having. I definitely understand changing the background is one of the most common and rudimentary tasks in a presentation software. While there are tons of different ways you could implement that function, they did try to make it as simple as possible. You have the Change BG button when working with a cue, or you an drag and drop to change the BG (drag from Windows explorer onto a cue). Your feature request can definitely be added by posting here:
I've used many different presentation softwares and honestly though I can't say there's really an easier option I can think of, so I think that is important to remember when dealing with the frustration from volunteers. Even in Powerpoint I don't think it's any easier, and even if so I would struggle to see how that one element in Powerpoint would negate how much better and easier just about every other function is that you get in Mediashout.
For now I would suggest doing it by dragging and drop it for the fastest way to change multiple ones at once. Or you could copy and paste however many cues into a new script and use the Change BG > For this entire script option and copy and paste them back. Here's a quick demo video on how I'd do those: