The cost of providing such mechanisms and properly securing them against abuse have to be weighed against the benefit. In order to know the benefit, we need to know the size of the problem we are seeking to solve, and whether or not the proposed system would actually solve the problem. So yes, knowing the size of the problem matters a lot, and is a good first step to running a cost benefit analysis.
Excellent, since you wish to run a cost-benefit analysis you can first start by citing the research you used to conclude that the abuses of the current system are small. That would give us a baseline for analysis.
It is then easy for you to take the first step in the cost-benefit analysis you wish to do by estimating the costs. The proposal is that a court order demanding disclosure, which are already routinely issued, can not be stalled indefinitely through the application of lawyers. So, all you need to do is identify the balance of cases where disclosure is fought and then see how often the disclosure results in illegitimate harm to the disclosed party versus how often it results in the discovery of legitimate harms caused by the disclosed party.
The disclosures in the Panama Papers alone resulted in 1.2 billion dollars of recovered taxes [1]. So you can compare the estimated costs against the benefits of preventing a singular incident for now. If you can present credible evidence that the harms of requiring disclosure on legitimate court orders is in excess of that, then a broader analysis of the problem size if warranted.
They didn't volunteer to do your homework. You were originally asked for a citation on
> frequently abused to not only protect privacy, but to protect against legitimate legal need
Shell corporations are used for unsavory purposes being a meme is not proof of this as was implied by your other comment. Also 1.2B in taxes is pocket change so it doesn't really help your point.