That seems like what stock compensation is aimed at. If the company gets a better deal on something, it retains more of its assets and is thus worth more to its owners.

Yeah, but the stock price is affected by too many factors to make the argument that it's a good proxy for any one thing.

Certainly, the stock value isn't going to rise or fall appreciably for most of the deals that the CEO will negotiate - it would have to be big enough to 'make the news' and/or show up in a press release, at a minimum.

I feel like I've heard the argument that "CEOs negotiate great deals and that helps to justify their compensation" before, but I've never heard of anyone actually basing a compensation schema on that directly. Given that we live an an Era Of Data I'd expect companies to be doing this (or trying to do this).

The stock price is what the investors value; they want the CEO to increase it by whatever means. Any other incentive structure would presumably lead the stock price to fall, or rise less, which wouldn't be what they want.