...that's really no different than how things are today - most CEO's are compensated based on the stock price performance which is correlated relatively well with profit.
The problem here is illustrated pretty well by a situation I witnessed: the CEO had a contract, somewhere in the neighborhood of 5 years at which time he was supposed to get the stock price to $65 (or something like that) from the $30 range it was at when he came on board. Our intrepid CEO, working with the Board and the Stock Analysts more or less cooked the books (completely legally and GAAP compliant mind you) to get the price there during that timeframe - showing significant revenue and profit growth rates through fundamentally unsound business practices (i.e. signing bad deals, doing quarterly layoffs, and a host of other completely legal "tricks" to get the balance sheet looking the right way for the analysts).
He made his target price, received his bonus per his contract that the board had negotiated, and a few months later the growth rates that had driven the stock price up stalled - and the bad deals finally came to light as our cash flow went into full crisis mode. Our $65+ dollar stock tanked to around $10... and the board sent him packing with his ~$30M bonus (that he had quite clearly, and legally earned through the terms the board put into his contract) fully intact.
That's the problem here. Lets say Ballmer gutted Microsoft's R&D... on the short term that would make the balance sheet look really good, and if the analysts/board/public didn't really catch on to the long term consequences that could make the stock price go up - it absolutely would make the profit margins go up regardless, so in at least one scenario there's a good chance that basing compensation on profit is potentially worse than on stock price.
The problem ultimately is that the boards and the execs want performance incentives in the contracts - and there's really no good way right now, IMO, to judge the long term soundness of an exec's performance. Stock price, which is what is typically used, is probably the best holistic yardstick... but it still fails as the balance sheet (which is about as far as most analysts go) is just a point in time snapshot, and it can be gamed quite successfully.