Why?
Honestly, how would that be bad? After all the UK consists of Wales, England, Scotland and N. Ireland. People of the past opposed that unity so much they were willing to die to try to prevent it yet on the whole that unity has been undeniably positive.
For the EU for example, how could having an single foreign policy be a bad idea in any way? How does having an EU flag do any harm what so ever? I'd claim that point in particular shows the issue very much is emotionally driven.
And what will make it fall apart except people voting to leave it on grounds as trivial as having a flag?
Likewise such an extreme step as dismantling the entire EU project rather than just fixing the monetary problem can't really be justified rationally and looks pretty overwhelmingly like emotionally driven nationalism.