It is indeed a way of routing that fits very well with that kind of circuit, but only with that kind of circuit.
That looked like a very pragmatic approach to PCB design that can solve most if not all wiring.
Is it a well-known method? Any advantage or downside you would see for it?
What is your opinion?
So the method is well-known, that's clear by now.
It does not solve "all wiring". It does not make much sense for discrete analog circuits, where most footprints have 2 or three pins (resistors, capacitors, transistors). Analog circuits quite often also have severe constraints for voltage drop due to current through PCB tracks. Forking of a T on the wrong side of a track can ruin a design, especially where high currents and sensitive inputs come together in products such as for example audio amplifiers. An audio amplifier can have 10A (or more) currents though it's power and output section, while the input is around 1V max, but also with a dynamic range of 120dB or so, which means signals down to microvolts are important.
And indeed, also by high pin count IC's that kind of routing simply does not work. IC's with 1500 pins are not exceptional, and for those you need multiple layers just to get the tracks away from it. And with today's much higher signal frequencies, signal integrity is a much bigger concern and things like differential pairs and length matching for bus signals is mandatory. Quite often it does not matter much how long a track is, but via count is reduced to a minimum for a lot of signal tracks because they cause impedance mismatches because of their irregular shape.
Also note that an IC with 1500 pins is quite likely to have 200 or more pins (pads, balls) just for GND and power, Decoupling of the power is very important. High end PC processors can have a TPD of 200Watt or more, while the core works with a voltage of around just 1V, and that is more then 100A (over different power rails) going to and coming from such an IC. 100mV ripple on the power supply probably also kills the whole thing, while 500mVpp of ripple does not matter at all for those old TTL boards.