There have been several studies that more lanes tend to lead to more traffic, not less. Here's a wiki article about the phenomenon:
https://en.wikipedia.org/wiki/Induced_demand
Wrong. More lanes doesn't lead to more traffic unless there are way too few lanes in the first place. I know of plenty of places where adding more lanes would not add more demand - North Dakota is full of them for example.
The only problem is we can't afford to build enough lanes. There is a limit to how wide you can go, and up or down is vastly more expensive than at grade. We could do it if we wanted to spend the money - but most such places find that a better bus and (not or!) train network is a better investment.
That's not necessarily a bad thing by itself. It means more people get to go where they want to go. But of course that can cause some negative externalities.
Creating more throughput instead of a quicker route isn't the same as saying "more lanes do nothing." So maybe your new highway lanes didn't cure congestion, but they did help alleviate housing demand some by letting more people commute with the same (albeit bad) commute time.
