If he was performing well in terms of "putting up numbers", but treating his (and Larry's) employees terribly to do it, firing him would still in my opinion be the right move, and would certainly not make Larry an asshole.
I agree. Sadly these days, performing well is almost invariably defined in terms of "putting up numbers". The issue of treatment of employees comes far later (and far meeker) than the issue of making profit for the shareholders.
And, excuse me for saying that, that's why you're not a CEO of such a large company.
Consider these alternate (admittedly extreme) realities:
A. CEO is an asshole, but manages to bring in $1M/employee in revenue for a company with 500 employees.
B. CEO is a nice guy, but doesn't manage to bring in enough revenue and has to fire 250 of 500 employees.
In reality A, those people who don't think they are paid enough for the abuse, will leave, as they should. In reality B, the choice of who leaves and stays is almost random.
What you say is that firing a reality A CEO is "the right move". The problem is you're extremely likely to get either a reality B CEO, or an asshole with reality B revenue. HP's history since Carly Fiorina would give you a good case study.
So, from almost anyone's perspective, armchair generals excepted, it is NOT the right move.
Obviously I'm not a CEO of a Google-scale company. I am a CEO of a small software company, fwiw. But it doesn't really matter. You may be right that choosing not to allow employees to be treated like garbage would be a poor financial decision in some cases. I would still classify it as the right decision, but I can see there being an argument there. That said, there would be many, many highly qualified applicants to a position like CEO of Nest, and it would surprise me if it wasn't possible to find someone who was both a) at least as competent as the outgoing CEO, and b) not abusive to employees. In that case, it would also be a (potentially huge) financially beneficial move as well.
Edit: oh, and to my original point - in no scenario I can think of would firing someone for abusing their employees or co-workers make one an "asshole".
Of course. Neither would I (act like a sociopath or ever be CEO of Google or anything 10% of its size).
But we should not be ignoring the reality, which is that many CEOs are sociopaths (as are many successful politicians). Larry Paige is not, as far as I can tell, a sociopath, but because he does actually have to report to shareholders, he is unlikely to fire someone like Tony Fadell for mistreating his employees as long as he delivers. Fadell didn't, and that's why he's out -- not because of how he treated his employees.
Reality C is far more common - CEO is an asshole and clueless about running a profitable business. Because they're too busy and distracted by self-important posturing and/or outright fraud to make good decisions.
Competent assholes are far less common than incompetent assholes.
There's a bizarre myth that being an asshole somehow correlates with business competence.
But that doesn't take any account of the large number of asshole CEOs who are crash-and-burn fuck ups.