EU referendum, brexit and the aftermath

What would it profit the EU to allow a delay, if both parties are the same with regards to the EU relationship?

I gave two reasons, although they're just my best guess.

It'd be referendum vs GE, would the DUP prefer to remain in an alliance with the government in power rather than accept the Irish sea border that would result from a Labour GE victory?

I'm not the DUP, but I would say absolutely no. They would not rather remain part of the government in the face of a sea border. Which is what the referendum risks Why would they support a referendum that threatens Northern Ireland's position in the UK? How could they?

One reason, surely?
Reason 1. rise of Eurosceptic parties: I'm guessing you mean that the EU being seen to allow a country some time to have a GE would be a demonstration of reasonableness, and to do otherwise would be ammunition to be used against them, so it's effectively the same as 2. because it's the right thing to do.

If you the DUP what the only route forward that works for you is no-deal. The party most likely to deliver that is the Conservatives. If May's deal gets voted down and she has no follow up move, then it's a GE and a border in the Irish Sea with Corbyn. A referendum on deal vs no-deal is the logical next move for May, and because the alternative might be Corbyn the DUP's least-worse choice is to support it and hope that the public votes for no-deal. To do otherwise gets them the Irish Sea border by default.

Post deal vote branches (feel free to add more):

1. Deal is approved, proceed to Brexit
   
2. Deal is voted down, May has nothing else, GE, Corbyn, deal is approved, proceed to Brexit
   
3. Deal is voted down, May has nothing else, GE, Hunt, deal is approved, proceed to Brexit
   
4. Deal is voted down, referendum, no-deal gains mandate, DUP happy