This is primarily for ease and feasibility of routing. If you keep all routes vertical on one layer, all routes horizontal on the next, then you avoid a wide class of situations where you metaphorically paint yourself into a corner.
Nets that need to cross have a clear path to do so, by either a via going up or down to an adjacent perpendicular layer, but more importantly, if you're running a long distance vertically or horizontally, an impassable (perpendicular) obstruction on the same layer is much less likely to be possible. If you have only vertical wires on a layer, you never hit a horizontal obstruction on that layer.
For analog design, the design principle I happened to use was:
- Local routing, short runs in any direction necessary, on M1
- M2 would run horizontally, often carrying gate signals between parallel fingers of a transistor
- M3 would bring in sources/drain signals and connect to M2 to reach gates for feedback/cross-coupling in the same cluster)
- Further layers would provide interconnect between these transistor clusters.
Here's a partially annotated layout showing this in the switching quad of an active mixer:
As described above, M1 is used for local interconnect (poly-M1 vias to the point where they reach their horizontal rails) and odds/ends (connections to the guard rings, dummy transistor routing, etc). M2 carries the gate signals (the IF of my mixer), while M3 brings signals into and out of the cluster.
Outside of the image (above and below), M4 would be used to interconnect same-net M3 lines, although I could have done this interconnection on M2.
The result is as described above - most signals get clear runs for a significant distance, and when they do need to cross, there's a clear path to actually crossing on the next layer. There are no situations where a signal just runs into a dead-end (which would entail doing a lot of rip-up and rerouting).
Note that unlike the topic of your quoted paragraph, which discusses a floorplan for a digital circuit, this is a local slice of an analog circuit. However, the principle still applies.