Approximately Optimal Mechanism Design vs. Revelation Principle The abstract of the article "Impossibility Results for Truthful Combinatorial Auctions with Submodular Valuations" (Dobzinski, Vondrak, 2016) states


  A long-standing open question in algorithmic mechanism design is whether there exist computationally efficient truthful mechanisms for combinatorial auctions, with performance guarantees close to those possible without considerations of truthfulness. In this article, we answer this question negatively: the requirement of truthfulness can impact dramatically the ability of a mechanism to achieve a good approximation ratio for combinatorial auctions.


My question is--  given that the revelation principle says we can WLOG restrict our attention to direct-revelation IC mechanisms in mechanism design, how can there be a loss of revenue/lower approximation ratio by restricting the search of approximately optimal (i.e. revenue maximizing) mechanisms to IC ones?
A key part of the paper is that they are interested in 


  computationally efficient truthful mechanisms


The VCG mechanism is a truthful and efficient direct mechanism, but it is not computationally efficient. In many combinatorial auctions, it is impossible to compute the VCG transfers in a reasonable amount of time using current technology.

In the past, economists have largely ignored the problem of computational efficiency in mechanism design. This problem has been mainly addressed by computer scientists. Read for instance the introduction to Milgrom and Segal (2020) Clock Auctions and Radio Spectrum Reallocation. JPE