Not exactly. Recent college graduates still know what an org chart is, and most corporate professionals are still promotion-focused, which wouldn’t be the case if there were no positions into which to be promoted. And at many companies, if you bypass your manager to share an idea with a higher-up, you’ll probably get in a bit of hot water.
However, organizations are certainly flatter than they were 20, or even 10, years ago. And research indicates that this is not necessarily a good thing.