This is false, though. The method of growing doesn't affect the feasibility of public transport: the density of the areas in question does.
And no matter how the areas grew, an economically growing public transport network will naturally connect the most dense parts of a city together. That is, provided there are dense areas. Think London's 100+ year history of the Underground where underground railway companies, as soon as funding was secured, built little stretches that made the most economic sense.
Also I believe the dead space problem will take care of itself as demand for space increases.
It doesn't if the environment doesn't lend itself to grow, change, and adapt as needed which is a big problem with designed areas. An area also needs both old and new lots and buildings to offer space for businesses that wouldn't survive with market rents. This is something nobody can design.
You're quite never sure of that. Just yesterday evening I was walking down on a street in my city (East-European capital) whose 19th-century buildings were raised to the ground around 25 years ago. There are still un-developed patches of land on that street, which, needless to say, make it look deserted and desolate even though it's only a 5-minute walk from the Prime-Minister's office building.