> It is completely irrelevant, ecologically speaking.

How so? It makes the box unrecyclable; worse still, as soon as such an item is detected in the recycling plant it will often cause the whole batch of material to be rejected and dumped[1].

No-one has time to pick-through cardboard removing batteries and circuitry.

[1] Source: anecdote from a colleague who worked in a 'recyclarium'. Contaminated material causes the line to be stopped, batch dumped and machines cleaned.

The actual pre-processing sorting is quite fascinating, using spectrometers to detect the type of materials.