You aren't paying attention.

No... I am paying attention. I just disagree with you. Let's keep the condescension out of this, okay?

But now, instead of slowly phasing some out and phasing some in, now they've all been challenged and the agreements between the EU and UK are about to be cancelled.

The EU-UK trade agreements are unlikely to be cancelled until new ones are put into place. It wouldn't benefit anyone.

EU-UK trade today is the same as it was yesterday. But when they push the button on Article 50, it won't be

Article 50 isn't a Big Red Button that suddenly nukes all trade agreements. In fact, it's a fantastically vague section of a treaty, which means that exactly how Brexit will work after Article 50 is invoked (whenever that happens) will be up to the UK and the EU, and I doubt that either side is going to go for an option that causes a sudden drop in trade between them, considering that both sides benefit from that trade.

And meanwhile, every other member state is going to fight this very battle.

Maybe. Maybe not. Undoubtedly separatist/nationalist parties will get a bit of a boost for a while, which may or may not continue on depending on how exactly Brexit pans out for the UK. But referenda take a long time to put together, and the UK was arguably much better-positioned for an exit than a lot of other member states. It remains to be seen if the extra boost actually gives other member states the kind of momentum that they would need in order to get to a referendum of their own, much less to vote Leave.

A strike authorization is where bureaucracy gets really ugly. Meanwhile, work continues apace.

You've been arguing that the first sentence is key. I have been arguing that the second sentence is much more important than the first. Work will continue apace, despite the new bureaucracy. Will the bureaucracy get ugly? Possibly. As I said, Article 50 hasn't even been invoked yet, so I'd say it's a bit premature to make calls on how the logistics will play out in the long run.