Driving to work is the most common way of commuting everywhere in the US except NYC. So in that sense, no, taking a taxi to work daily is not normal, just as walking, biking, and taking public transit aren’t normal.

When I worked in San Francisco I took Caltrain to the city, but I took Waymo from the train station to the office. San Francisco, like almost all US cities, has poor local transit coverage. In my case there was a bus that took a similar route, but it only ran every 20 minutes even during commute hours and wasn’t coordinated with the train, so if everything was running on time it would have been a 17 minute wait (plus an extra 5 minutes walking). I was busy and well paid enough that spending the extra $10 to save ~20 minutes of travel (and the uncertainty of when the bus would arrive, and how strongly it would smell like piss) was well worth it.

San Francisco's connection to Caltrain is deplorable, but as far as US cities go, the heart of it has pretty good public transportation.

not everywhere in the US except NYC. People take trains in Chicago, for example.