IKEA already did that. Creating 80+ local language instructions were a pain and an expense, so now all of them, or almost all of them, are completely comic-strip-like without a single line of text.
A comic-strip depiction of how to put something together is much different than a single symbol standing for the entire process.
This is a marvelous example of how these symbol things should work. The Japanese washing instruction label at the top of the page contains four symbols, NONE of which match anything shown later as the standard. The closest is the "do not wash", but the label has a red X and the standard is black.
The "natural drying" icons are not very obvious, either. The "line dry" kinda looks like "put in an envelope". The "drip dry" looks like "hang over the heater vent." "Tumble dry normal" looks for all the world like "you need to keep close watch (both eyes) on the dryer or the clothes might go up in flames."
"But I don't want to have to learn all of these things!" You don't need to. Simply print off the local-language version of the ones you need and place it in the area it is needed.
Exactly what would be the "area it is needed" for a list of the icons that stand for food allergies? Most people don't do laundry outside the laundry room, but people tend to eat stuff anywhere they are. Where would I find a translation for "peanut symbol" to "I have a deadly serious peanut allergy" when I'm sitting next to someone at a Laker's game with a bag of peanuts and they're busy pointing to a peanut tattooed on their arm? Or would I assume a peanut tattoo means they like them alot and here, have one?