This is simply not the case in Switzerland. Most people take the train/tram if it is not reachable by bike.
The US has pretty good public transit in the places that have merited it prior to the widespread adoption of the automobile. If the city was large relative to its size today (geographically) in the early 1900s odds are good it's got acceptable to good transit.
The places which have mostly grown after the 1940s tend to have poorer transit as cars came to dominate.
Comparing what works in Switzerland with what works in the US doesn't make that much sense, though. There are plenty of stretches of railway in the western US that might be hundreds of miles between places big enough to warrant a substantial power station. Which means that you're going to have to pull hundreds of miles of high voltage lines (which aren't free) in order to have a stationary power plant power the all-electric locomotive. Or you can just drag around your own power plant, sans wires everywhere; a diesel.
There are other systems that do, though: PATH (for points immediately across the Hudson), NJTransit (commuter rail to a lot of NJ), LIRR (commuter rail to Long Island & Queens) and MetroNorth (commuter rail to points north in NY and CT).
Given how long it takes to ride the subway to the farther reaches of Queens (e.g., Jamaica), I can't imagine how long it would take to commute to Manhattan via subway from, say, Bayside Queens (which is served by LIRR).
Also there is a lot higher traffic densitiy in main lines in Europe which also justifies the cost for building and keeping the infrastructure.
The problems with electric trains is needing to supply and maintain catenaries, needing to source enough power, and needing to cope with highly variable electric demand (trains use much more power when they hit a steep incline). In the early 20th century, when railroads were replacing their steam locomotives, the rural electrification projects in the US just didn't exist yet, which made electrification of mainline railroad track quite expensive. The few railroads that tried ended up bankrupting themselves in the process.
Another drawback of electrification that's only obvious in hindsight is that installing catenaries makes enlarging the load gauge that much more costly--if the US had mostly electrified its freight track, it likely would have never developed double-stacked container trains (absent in much of Europe since the electrical catenaries provide insufficient clearance), a development which did much to revitalize the railroad industry.