Maybe nobody has thought of asking for this before.. suggest it here and in the Feature Requests thread, and you're more likely to get it implememted. I think it's a good idea, even though the fireworks sound (exclusive to the Roku 3, I believe) doesn't bother me.
Maybe oversight is a better word. All kinds of devices make noise upon bootup, but I certainly wouldn't care if that boot screen went away.
Curious about the set up - is her TV automatically set to the Roku input when it powers on, or is it a case of "last input used"? Also, does she need to save power when the Roku isn't being watched? From the reports I've read, the Roku barely uses any power even when streaming, and as low as one-two watts when "idling". My point is that you're not (most likely) going to get a fix on the startup sound, so perhaps the workaround(s) need to be employed.