Given we import more than we export you could argue this the other way, a free trade agreement is mutually beneficial to EU and the new free independent UK.
Classic muddled thinking - it doesn't matter that we import more than we export, the issue is what proportion of our trade is with the other 27 and what proportion of the other 27 is with us. So trade with the EU is proportionately far, far more significant to us, than trade from (for example) Germany is with us.
Try it this way - image I am a small company with a turnover of £1M and 50% of that turnover depends on bilateral trade with Tesco, and they buy more from me than I buy from them. So £500k of their trade is with me, which represents 0.0008% of their turnover. Who is the deal more important to - not rocket science. Now I now this is a more extreme example than UK/rest of EU trade but the principle remains trade from the other 27 with the UK represents a vastly small proportion of their trade or GDP than trade from UK to the other 27 represents for the UK.
So we are screwed if we don't get a deal, for many of the other EU countries it would have very little effect. And for some there is very little trade at all - Bulgaria, for example. And there may be other issues far more important to the Bulgarian government and people than a tiny loss of trade, for example free movement of labour.
But of course Bulgaria has an absolute veto on any deal, so if Bulgaria decides not to play ball unless the UK allows free movement, then the deal is dead and up come the tariffs once the 2 year moratorium is over and there is absolutely nothing the UK can do about it. Indeed this is why there remains no deal in place with Canada, despite Boris (never one to actually understand detail) claiming that was the kind of deal we wanted, i.e. one that isn't in place 8 years after the start of formal process and 12 years after the agreement to sort out a deal. And of course one that even if enacted it doesn't cover services, which just might be a teeny, tiny problem for the UK.
There is also, of course, the politics. There will almost certainly be countries that will want to give the UK a very hard ride if it leaves, on the basis of deterring others from leaving. Now you might think that's pathetic, and silly, but your view is irrelevant - if Portugal for example thinks holding the EU project together is more important than a bit of trade with the UK, then we are in trouble. And of course this is what the UK government did in advance of IndyRef