You're kinda looking at it backwards, it's not that the EU wants a more complex relationship, it's that the UK is after a much less complex relationship than we currently have.
Of course the big issue is still that the only reason Canada ever got a "Canada style deal" in the first place is because they're six thousand kilometres from mainland Europe, not thirty kilometres from mainland Europe and sharing a border with en EU country like the UK is. This is the big issue that our government keep ignoring/dodging while they rave about an impossible Canada deal in order to give the illusion they're actually trying to get a deal done (and the complementary illusion that it's the EU being awkward).