Interesting. Hatchobori (being in Chuo-Ku) is definitely central enough for there to be no problem, and that there is on weekends surprises me. It is admittedly a slower area on weekends than on weekdays but a quick look at the Go Taxi app yields a wealth of possible pickups there. That alone tells me that the access is there, but the drivers are trying to make an extra few yen by waiting to be called vs. driving around in search of rides. In other words app use is becoming very normalized and preferred by many. So much so I wish they would just turn of the "reserved" light when in a reservation call rather than having the orange lamp lit. I would be extremely surprised if there were no taxis at or passing by the station though. I would expect to have to go much further from Tokyo station for that. Regardless of the area, waiting in front of one's apartment building is and always has been a less than ideal strategy to grab a taxi compared to strolling down to the station.

I live in Meguro and there is zero issue here. I work in Minato-ku near Roppongi and there is zero issue there. I also work in and around Toranomon and have never waited more than about 30 seconds there. Of course I try to position myself on roads that lead to/from nearby stations//places of interest/ hotels etc.

In Meguro if it proves challenging (i.e. weekdays 7:30-8:30am etc) even on Komazawa-dori, I will walk to Yutenji, Naka-Meguro, or Meguro station and there I wait no more than 30 seconds. Hopefully this veteran advice will help.