20 meters a day is 4 km/year assuming you only work weekdays. (This is a bit faster than average, but not unreasonable). In your city you only need a pit every 4km, which is a lot easier to find, you don't have to be exact (in fact you don't want to be because you probably need more crew to pull them out at the end of the tunnel), so you can find an outdated building to buy for cheap someplace along the route. Or you can do a two year dig with 8km access holes. Don't forget that you need a station someplace in the city - your large hole to get the machine out in the middle of the city should be planned where you need the largest station anyway.

Of course for mountains and large water bodies you are correct. The English channel left some TBMs in the middle so they could get done faster - at much higher expense.