That won't do you any good. Any large piece of copper floating over a ground plane is a resonator. The capacitance between power / ground planes is highly overrated and the inductance of a power plane is underrated. So having the power and ground planes on the inner layer is better and the power plane needs to be AC coupled to the ground plane. That at least provides isolation (less crosstalk) and a good reference plane to the signals. If you want to route high speed signals over such a 4 layer board, you'll need to add decoupling capacitors at places where you go from top to bottom (=from ground plane as the reference to the power plane as the reference) to carry the return currents that move along with the high speed signals.
Who said anything about "large piece of copper"?
If you mean the fact that there's two planes at all (then, I guess, advocating routed power over plane?), simply spreading around some bypasses (chosen appropriately so that ESR dampens ESL * plane capacitance) handles that effectively. Which can be easier said than done when you're stuck with ceramic capacitors and no room (in terms of ESL) to add a resistor, but, in principle anyway.
Or given the proposed application, not much plane area might be needed anyway, more just to get some room between active device(s) and bypasses. Or excessive plane area might indeed be discouraged so as to avoid subtle bouncing of a desired very-flat square pulse.
Actually not. Capacitance and inductance are basic physical properties which don't change regardless of frequency. You can not change the laws of physics. Simulating these kind of structures using an EM field solver like Sonnet is extremely insightfull. 15 years (or so) ago some guy in SED (who appeared to be considered knowledgable by the other inhabitants) claimed that connecting top and bottom RF ground planes using 1 via would be enough and capacitive coupling would do the rest. So I put that to the test and build a simple LC filter using SMD components (around 700MHz IIRC) on a double sided board. Long story short: the filter didn't work at all until I added way more vias to stitch the top & bottom grounds together. To verify I simulated the same structure using Sonnet and it quickly became obvious that the top & bottom ground planes behaved like resonators when not stitched together properly. And this happened at several hundred MHz!
It's right and wrong, depending on perspective. It's clearly wrong for the wideband case. It's right above cutoff. Or... has the greatest chance of being right above cutoff. I mean, there is termination required, the plane plus via looks like a 2D shorted stub and you get all the modes between them (plus radiation off the edges like an open waveguide), and that all needs to be bypassed or dampened out to get a flat impedance. But the impedance is also very low (some ohms, for close plane spacing and wide dimensions), so even with resonances, the peak impedance might be low enough (say at some given via pair anywhere on the plane pair), that you can get away with, say, bandpass microwave structures on top, in the 50-100 ohm ballpark. It's not going to be a good design... but just to say, it might work.
The better reading of such advice is, it was woefully over-general, for something that is a very special case, with a lot of provisios that might've been assumed rather than indicated (like the necessity of bypasses or termination). From which we can conclude, the person proposing such, is either not as smart as they claim to be, or is more popular / seemingly trustworthy, for political rather than technical reasons (always an important consideration in any community).
No, capacitance and inductance are not fundamental. Electric and magnetic fields are fundamental.
What we term capacitance and inductance are a simplistic description of some of the interactions between those fields.
I mean, you can keep using L and C, and Kirchoff, on differential elements within the field. But that's just FEA with extra steps, and relegating them to lower-frequency or narrow-band lumped-equivalent modeling, is probably the more responsible application.
Tim