> But those extra people are choosing to be there so there must be some benefit.
As long as your roads are saturated, they have less throughput, not more. It is kind of like a clog in your toilet: more things are there in your pipes, but not much is getting through.
A clogged toilet isn't flowing. More like dumping a 5-gal bucket into a sink . The drain is running at full capacity but any one drop may take a long time to actually clear the sink. The 5-gal bucket is peak demand. Total time to sink clear is how long rush "hour" lasts.
Fluid analogies are crappy because fluids flow more when you add pressure and traffic doesn't.
If your city sewer is clogged, so you widen it, then more people install toilets in their houses and bring the sewer back to capacity, I think that's still a win.
As long as your roads are saturated, they have less throughput, not more. It is kind of like a clog in your toilet: more things are there in your pipes, but not much is getting through.