I absolutely agree. I think that a sponsor, before they can be eligible to go into the lottery, should be pre-screened. The solution is a matter of linking their tax information. On a citizenship application you can link their tax information through the use of their SIN and their permission to link. You don't need to require the submission of the notice of assessment.
For sponsors who have filed income tax returns for three years, you can get tax information quite easily and, based on the income tax documents, you can determine whether they meet the eligibility requirement for the LICO. I think that's an easy, quick fix the department could look into.