Unfortunately it's an exceedingly complicated problem since a number of the main roads through town are actually US/state highways and as such, modifications require coordination between local, county, and state agencies, and often involve almost unbelievable lead times.
We have nearly a century of data on this. It was observed when Robert Moses tried to build more parkways in New York, it was true in Texas and LA, it was true everywhere.
"Traffic is already bad" is a common NIMBY line in my area, but traffic will always be bad with sufficient population. Building more roads will not change that.
Yes, it's technically affected - both in the "if you build it they will come" sense and that if transit becomes sufficiently congested people will change their transportation behavior - but cars have more liquidity and hit traffic limits much easier.
The university that dominates my college town does not give a fuck about housing or infrastructure support. They are growing enrollment regardless. The kids who have to drive to campus rather than take the bus because there isn't enough housing within bus route distance are a pretty big problem for congestion.