Electronic – Why put vias underneath an IC

I actually prefer vias as testpoints for just the reasons you mentioned. I think it makes using a multimeter or a scope probe much easier. Which, after all, is the main use of testpoints.

Where possible/practical, I like to size my vias large enough or use small plated through holes so that 30 gauge wire can easily be soldered in. Then I can clip a scope probe to the wire and have my hands completely free to operate a computer or other test equipment.

The reason not to use vias and especially not to tack wires on is the additional inductance and capacitance that such features would add to the trace and therefore distort your signal. This is of great importance when you're trying to measure high speed signals. Here is a good article on calculating via inductance.

$$L_1 = \dfrac{\mu}{2\pi}2h\cdot ln\dfrac{s}{r}$$

Where:
\$\mu = 4\pi\cdot10^{-7} H/m\$ - the magnetic permeability of free space
\$x\$ - the radial distance in meters away from the signal via
\$s\$ - the separation between vias, center-to-center
\$h\$ - the separation between planes 2 and 3
\$r\$ - the radius of the via holes

Keep in mind that this formula makes some assumptions that the author notes and is therefore just an approximation:

This formula for L_? is a gross approximation that glosses over the position of the returning current path, a simplification I greatly regret not making more clear in the book. It makes the crude assumption that the return path is approximately coaxial and located at a distance s=2eh, where e is the base used for natural logarithms. When the inductance really matters, a more accurate approximation is needed.

However, the article Test Pads on High-Speed Nets points out the problems that that form of instrumentation can cause.

If the signal is on an outer layer, it’s not possible to place a 35 mil test pad directly on a 5 mil wide trace without creating a PCB routing nightmare. Differential signals are intended to be closely coupled, and the radius of the test pad will create additional routing constraints where they are already likely to be over-constrained:

Instead they recommend using non-intrusive technologies when trying to measure high speed signals. Which leads me to believe that, on signals that can handle the additional inductance and capacitance of a via, there is no reason to use a test pad given the benefits a via gives to using a meter or a probe.

This is my understanding, based on very little knowledge:

The the return current for the high speed part of the signal will take the path of least inductance. This means travelling along whichever plane is closest to the track. (In fact, it will travel on the side of that plane closest to the track).

When your signal track moves from the top layer to the bottom layer, the return current will want to move from one plane to the other (whichever is closest to the track). If these were both ground planes, then your second image would be fine. You can simply connect the two planes together with a via. But in your third image, you can't connect the two planes together with a via, because this is a short circuit.

If only there was some way to allow the high speed part of the return current to move from one plane to the other, without shorting out those planes. If only there was a component which conducted high speed signals, but blocked DC current.

Oh wait, there is. It's a capacitor!

The return current will flow along one plane, then, when the signal track changes layer, the return current will come up one via, through the capacitor, down the other via, into the other plane, and continue following the track.

In fact, this is exactly what the diagram shows in the yellow arrows.