Among the top 100 offerings or so, the differences in quality of education are very small. The differences in quality of students are pretty small. But connections matter, and even if Harvard student's aren't all shockingly brilliant, the dumb ones are connected.
If you go the #147 private college and pay $50k per year, you'd be better served by a state school. If you're talking about Harvard, though... no, it's not a waste of money.
Perhaps surprisingly, the influence of pedigree increases later in one's career. These numbers are estimates, but an MIT CS grad might make $100k out of college while the state-school grad makes $85k-- not a huge difference. Ten years out, those numbers look more like $250k and $150k. Why? Connections tend to get stronger with time, even when not formally kept up. So much of the business world is run by nostalgia. That's why prep school connections are more powerful than college, and college connections are more powerful than grad-school connections... even though the elite high schools are less selective and meritocratic. Old connections suggest predestination ("born to lead") and, because of that, have a cachet that new connections (though carrying more signal) don't. The future may be (and most hope it will be) rich and abundant but the past is a scarce and eternally limited commodity; there will never be more pedigree.
Where you went to school matters not at all, ten years out, if you're in the top or bottom 10%, relative to where you might be expected to go with your training, career-wise. If you do really well, no one cares where you went to school. Or if you make terrible choices and fail catastrophically, the Harvard degree just makes it more pathetic. For that middle 80%, those connections made early on are going to start throwing "Get Out Of Jail Free" cards and that's a major asset if you want to break the ceiling and become a player.
I'd say that it generally works like this. From 22-25, pedigree matters a lot in an evaluative sense. (Make that 22-29 if you get a PhD.) From 25-30, it doesn't matter all that much because people have more recent data, when it comes to evaluation. From 30-40, it starts to matter again, not because people judge you based on it-- your record speaks for itself-- but because you're vying for leadership or coveted creative/architectural roles and that means politics, and you need "Get Out Of Jail Free" cards (which come from having connections) for when your risks blow up. After 40, it seems to stop mattering because that's an age at which you shouldn't need "Get Out Of Jail Free" cards at all.