From the outside (the US in my case) it looks like there's a lot of hate, but maybe it's just some well deserved schadenfreude. Everyone loves to laugh at Brexit voters.
I'm not so sure. The UK was a big contributor to the EU, not just monetarily, but it also gave the EU more soft power.
It was only Germany that contributed more, and in fairness, Germany also benefits more from the EU as well, although much of that is purely that Germany already had a healthy industrial sector, a central Europe location, and better transport links to other EU nations.
The UK and EU both lost out due to Brexit. And to think it all happened because of a stupid political gamble by Cameron. Infuriating.
And besides, I think it'd set a good precedent for the EU - look, even a country as wealthy and well-connected as the UK left then decided it was a terrible idea. Clearly it must be good to be in the EU! That's one hell of a boast.
That said, geopolitics is geopolitics. Various countries would be trying to carve out any little advantage they can get.
You're right and it is a real problem. But consider that the EU is a huge contributor to the stability of Europe, and the world as a whole. War between EU member states is unthinkable, that wasn't the case 80 years ago.