If counter-emf is zero, why is COE violated?
At a very high level...

What you're missing is relativity.

Your statement is true in a static frame of reference, but with charges in motion, you have electro-magnetic interactions. 

In a static frame (charges are fixed relative to each other), you can convert electromotive force to kinetic energy (and heat). However, in the real world, the conversion of electromotive force requires those charges to move... and moving charges disturb the fields around them.

Disturbing those fields creates E-M waves and those have to balance out to conserve energy. That's the source of "back/counter"-EMF in electromagnetics.