But even when they do, it's easier to handle traffic spread among dozens of stations spread out over 100 miles of track than to have all of those commuters drive to the city center.
Commuters don't all drive to the city center, they drive to 1000s of working places and arguably that's easier to handle traffic-wise than the traffic around fewer train stations (in one city!).
If businesses were spread out near major transit lines, that'd be another matter, but as it is now, the density is too low to serve well, transfers are a hard sell to commuters, no one wants to commute 40 minutes by train only to have to wait 15 minutes to transfer to a bus that takes another 15 minutes to get them to work.
VTA transit tries to serve a huge area with light rail, but everything is so spread out and there are so many stops that it takes forever, you can take light rail the 12 miles from downtown San Jose to Mountain View, but it'll take over an hour with 28 (!) stops in between. You could bike faster.
Indeed. And trains usually don't go from people's homes to their destination, so they typically cause traffic of some sort around train stations.