The mysticism around GSP (generalized second-price auction) for ads is absurd. In twenty years, for “p(click)*bid”, the p(click) factor has advanced from a simple ratio to huge neural networks. But bids? “Sort and take the second price.” "Somebody once won a Nobel Prize." Long story short, GSP doesn't have many useful properties in practice except that it's easy to implement and compute and it's a "standard."
Major problems with GSP are: 1) Useful economic properties depend on non-repeated, "stable" auctions of 1D ordered lists, which doesn't describe most modern media. 2) GSP gets mixed with a "complementary bid" to control for user quality, which also complicates any theoretical properties 3) It's still complicated to understand and requires layers of control systems.
We originally started as “Algorithmic Auctions” to solve ad auctions fairly, but we didn't find a market for this.