Hit the nail in the head. A growing company has plenty of opportunity for learning, promotion, making new things, and retooling old ones to match the growth of business. This means there are very few zero sum games, either at the IC or management level.

When growth stops, there's little chances to gain status by solving problems: Someone already has status, and really doesn't want to lose it. Those frustrated with the lack of growth, and who have good skills applicable somewhere else will leave. The people that stay are those that have fewer opportunities to find something better elsewhere. So when you see an architect/principal engineer that has been there for 15 years, you know they know that they'd not be hired at the same level anywhere with more chances of growth: Those people have already left.

This is why i understand the middle manager that tries to empire build: If you don't have growth opportunities, your top subordinates will leave you, and with them your group's performance.

There are other reasons to leave a company, like if you see good chances that you'll dislike your boss and they will remain your boss for at least another year, but the lack of growth will always be bad.