One Question About Brexit that Baffles Me

There must be a logical flaw in my thinking about Brexit.  Can someone please point it out to me?

The European Commission and the great majority in the Council of Ministers say that it is essential that the UK is not seen to gain from Brexit, so as to discourage others from seeking similar gains for themselves.  Angela Merkel spelt it out with disarming frankness: if the UK is seen to gain from Brexit she said, other nations will just want to do as they please.

Now, by "gaining" from Brexit these EU leaders mean the UK continuing to enjoy tariff-free trade with the other 27 EU nations without being required to allow freedom of movement or make contributions to the EU budget.  This, presumably, is what they fear other EU nations will demand if the UK is allowed to get away with it.

But if they fear that other members will go for it, they presumably think that other members will think that it would be better for them too.  But if that is true for any of them, it is presumably true for all of them, isn't it?  Which surely means, does it not, that if all 28 members left the EU with a deal that gave them tariff-free trade with the other 27, no freedom of movement and no EU budget contributions, they would all be better off than they are now?  They would all feel they had gained, not lost, from doing it.  In short the disbandment of the EU would be a gain for all 28, not a loss, yes?

Where is the flaw in my logic?  Is it that such a deal would only be a gain for some of the members not for all?  If so, which ones would be the losers and why?  Is it that the gains for individual nations would be a loss for them collectively?  That surely can't be so; if all 28 gain individually there can be no collective loss, surely?

Do they fear that the collective loss will not be a material/economic one but, say, a security one? But they have NATO for that surely?  If they fear NATO may not survive, it is surely vastly easier for European nations to sign a mutual defence treaty to replace or run alongside it than it is to try to evolve such a thing through a phenomenally complex melding together of nations into a single federal union.  By the same token, in-depth cooperation on intelligence is vastly easier to do through nation-to-nation cooperation than through such a process. Such cooperation predates the EU anyway.  Ditto scientific research cooperation.  Ditto major project cooperation.

Do they fear that the EU's synchronisation of standards and regulations would disintegrate leading to a loss of efficiency, rising production and trading costs and declines in GDP? Well, comparative global GDP growth figures do not suggest that their existence has so far been a gain.  Moreover each departing member would be at liberty to continue using the old EU standards and regulations if it felt that was the case.

So, can someone please tell me where the logical flaw is in my reasoning that tells me that all 28 members would be better off out of the EU; that the EU's leaders know this is so which is why Brexit bothers them so much, and that the reason they nevertheless want to continue with the EU is that they are fixated on the dream of a single European nation to rival the USA and do not care that its peoples will be worse off, not better off, in it?