There must be something wrong with the following argument; perhaps it is that the initial assumptions are unreasonable.
Assume there is a perfect market. And assume that over time, installations in the EU ETS get smart and learn to keep their emissions just within the cap. They know they have to because, irrespective of the EU Allowance price, the penalty for non-compliance means going out of business
Knowing this, on the last day before compliance the participants in the scheme would also know that the price of EU Allowances should be zero. It is just a question of getting the allowances into the right accounts. They would then trade over an exchange at a price of zero and within a few moments everyone would be in compliance at no cost. Assuming very low transaction costs and very high transaction speed.
Knowing that this would happen, no-one would bother buying during the course of the year.
To avoid the possibility of installations being able to comply in this way, we want to avoid moving towards a perfect market. We need unreliable registries, limited exchange of information, limited communication between participants in the system and a general lack of attention to the matter. Otherwise, over time, the price will always be zero.