Daas Yochid: If you walk in the street, it is normal activity on any day. Unless you are going somewhere very specifically, you would not use public transport. When you use public transport, you are going to work or shopping. It I very unlikely that you would just take a “stroll” on the trains! As you are very adept at finding sources in HebrewBooks, maybe you can look up his sefer.
NIsht: no question of ‘tchum” as we are talking about a very large city.
In fairness, I think he was dealing with people who might use cars to come to shul- hence, much better to take public transport. However, the point is that there is no specific issur and one could rely on this, “beshaas hadechak”.