I would also say it's not a good idea to burn bridges; which is what inevitably happens when you run around telling people the reason you're leaving is because the company sucks. They can't do anything about it anyway (see my original comment), and you risk coming off as toxic to people you might want to give you a recommendation later in your career.
Very few people think their company is perfect, and being able to be honest about a company's shortcomings without resorting to "it sucks here" and similarly unhelpful non-constructive criticism is a sign of emotional maturity. People leave all the time, for various reasons, and most places I've worked that actually conduct exit interviews are genuinely curious as to why high performing employees leave.
I hesitate to say they "care" because I think that gives the wrong impression. Everybody wants to make a little more money, get a little more freedom in deciding their priorities, get a little more flexibility in their hours, etc. So if you say your only reason you're leaving is that you want more money, they're probably not going to give everyone a 10% raise next quarter. But if you have well thought out grievances that can be addressed without spending millions of dollars or completely changing the structure of the company, I think you'd be surprised how willing executives would be to try and make things better.
