Building housing near transit isn't nearly as important as building offices near transit, if you want to make transit (more) viable.
I can easily drive to caltrain and walk to work from the station, if my office is walkable from the station, and my house is drivable from a station with sufficient parking. It's much harder to walk to caltrain and then drive from the station to the office.
But if everyone drives to the station, you need to build parking for them all.
Garage parking efficiencies run around 350 - 500 square feet per car. So if you are your spouse drive to the train separately, you're taking 700 - 1000 square feet of space. It seems better to build 1000 square foot apartments on that space instead of wasting it on parking.
I say, get rid of segregated zoning and build more mixed use residential+retail+commercial developments and put everything closer to transit.
But one thing that's cheaper than building parking lots and garages for thousands of cars is to use zoning to encourage developers to build dense offices and housing close to transit so you don't need to build parking at all.
When the parking lot at the transit stops are overfull, it's clear that people want to be there, so they might want to live there. But keep in mind that the caltrain lots also backfill for not transit parking -- event parking for SAP center and parking for Sunnyvale downtown.
If everybody drives 5 miles and parks at the transit stop, instead of driving 15 miles to park at work, that's a lot less driving.
When the parking lot at the transit stops are overfull, it's clear that people want to be there, so they might want to live there
I don't think that's necessarily true - there are lots of transit stops (even busy stops with busy parking lots) in areas where I wouldn't want to live.
I can easily drive to caltrain and walk to work from the station, if my office is walkable from the station, and my house is drivable from a station with sufficient parking. It's much harder to walk to caltrain and then drive from the station to the office.