Okay, so instead of waiting at the platform 30 minutes, it becomes waiting at my destination (e.g. restaurant, office, whatever) 30 minutes for everyone else to arrive or for the meeting/event to start because it is unprofessional to arrive late, so I must arrive 0-60 minutes early, dictated by the train schedule. Doesn't change the fact that I have to waste 30 minutes on average either way.
In many cases, running, biking, driving would all waste less time because I can leave on-demand, even if the actual transit time takes longer.
Public transportation needs to be either frequent enough (e.g. Tokyo, Hong Kong, Shanghai, New York, etc. where rush-hour trains arrive about every 1-2 minutes, non-rush-hour every 5-8 minutes or less) or on-demand (e.g. UberPool, autonomous cars) to cut the time waste.
That implies 1) the train or bus arrives and leaves at the station exactly according to the timetable and 2) you get from home to the station exactly according to the estimate.
In my limited sample group of one (1), these are rarely true.
The train usually doesn't arrive exactly on time where I live, but delays aren't so bad that I have to wait 30 minutes on average. And if it's a 4-12 minute walk to the station, as OP says, I'm sure they don't need a huge buffer to get there on time. Personally, I just make sure I have a five-minute leeway and I'm good.
There certainly must be places in the world where trains are so unpredictable that the average delay is 30 minutes, but (not having been there, I should say) Menlo Park and Palo Alto sound like places where trains should be a bit more punctual than that?
Not all trips are to and from locations on specific timetables, such as work. Sometimes you want to go from your house downtown, or some other location. There's still an average wait of half the train interval time. You can wait at the train station, or wait at home and travel closer to the arrival time (and hope you don't miss it), but there's still a wait involved. Sometimes you can effectively use this time, sometimes you can't. Acting like it doesn't exist isn't useful though.
In many cases, running, biking, driving would all waste less time because I can leave on-demand, even if the actual transit time takes longer.
Public transportation needs to be either frequent enough (e.g. Tokyo, Hong Kong, Shanghai, New York, etc. where rush-hour trains arrive about every 1-2 minutes, non-rush-hour every 5-8 minutes or less) or on-demand (e.g. UberPool, autonomous cars) to cut the time waste.