I think the point is that we're not really good at being random, but combining two uncorrelated "random" draws into one gets something that will seem pretty random without closer inspection.

The point is that if a player needs a 6, they will always pick a 6. It's hard enough for people to come up with something random, but even harder if they know what number they need. Put two people opposed picking a number like this and it becomes random ish.

Well, dnd is largely cooperative: if you want to get a 6, I probably also want you to have a six. And if we're not even assuming that we are motivated to produce random results, than I seriously question whether such a simple rule would fix matters.

You are probably a DM and get how it works. Get the dice out for effect - they are a weapon too!

The whole point of DnD n that is it is fantasy ie thinking and talking about something that is not real. How you deal with fantasy is up to you.

Worrying about formalality is generally not a good approach to dealing with phantasy for obvious reasons.

In a game like dnd, you can't trust the player to pick a random number. So two sides who don't trust each other can generate a random number together.