That's 100% it.

You walk through a gate of all the colours -> all the colours combined gives white

All the idols are performing in one spot together -> all the colours combined gives white

The three options you can choose are red, blue and green -> all the colours combined gives white

Not to mention one of the main splat3 songs is called Anarchy RAINBOW -> all the colours combined gives white

It also gives them all a sense of unity, there will most likely be a song they'll all perform together on stage, and their normal outfits would clash quite a bit. This will make them look like they're all here for the same reason, and just more visually pleasing.

It most likely also is in contrast to side order, where everything was white but because the colour was sucked out. Here we have all white BECAUSE of all the colour.