Its trully really fast, but I have doubts for which role this way of building is most efficient.
Looking at the replay you sent, it didnt seemed like you'd have one lvl7 finished around minute 35.
The other ways of building sure are slower, but since you have less mills to upgrade, you end up having a lvl7 sooner.
Even though having a bigger number of mills really fast is great, finishing a lvl7 as soon as possible is still more advantageous( only for early/mid-game).
Also, that way of building is really high-end, uses a lot of mana and also demands total attention.
Taking care of it + doing the stuffs necessary for the base seems very taxing.
Since I'm really lazy, I would only build that way when being a lumberer. Its just perfect + rep (Y)