Well, unless by "local" you mean within an inch or two.
Closer than that - millimeters, really, if at all possible. That's how I can see basically all existing circuit boards designed, local bypassing of all power pins that matter.
Oh, yes! This is a superstition that is very hard to break. I do it myself! It doesn't prove anything. I carry an amulet to prevent attacks by rampaging elephants. Works a charm!
I assume you've looked at the impedance curve for caps, no? At higher frequencies the inductance takes over and the impedance rises, making the cap pointless for decoupling. This is where you need ground/power planes.
Inductance is no magic, power planes are no magic, and capacitors are no magic. Parasitic inductance is simply caused by distance. Capacitors are just "power planes" tightly coupled in a small package with very high dielectric constant and minimized distance between the planes for maximum capacitance - and minimum inductance. If a capacitor is placed 2mm away from the device pin it is bypassing, it does no worse than power plane 2mm away from the device pin. You can build a small-value but physically large distributed capacitor from power/gnd planes, but the capacitance will be small, whereas local bypassing with largest value of C in smallest possible package - something like 1uF in 0402 - does the same, plus the impedance curve extends to LF way better.
Clearly, you don't understand anything I've said. The problem is that at frequencies above the SRF, the impedance across a capacitor rises until it is no longer useful for bypassing... at all! The capacitance of the power/ground planes is small, but is effective all the way into the GHz region. So when your bypass caps poop out, the power planes still do the job.
Why does the small capacitance value of the planes not matter? Because you need much less capacitance at high frequencies. You should understand this. I don't know why you continue to argue the point. But maybe you don't understand. You say, "local bypassing with largest value of C in smallest possible package - something like 1uF in 0402 - does the same". But this is not true, which you would know if you ever looked that the impedance vs. frequency curve of the caps you use for bypassing. Have you?
You can calculate low Z for a power/gnd plane pair modelled as a transmission line until cows come home, but you can't connect that inches wide transmission line into a device pin, so it does not matter. The connection to device pin (plus the via to the plane) is the bottleneck, and as a result, power plane gives very little of that low-ESL capacitance, just some picofarads. More capacitance is further away, after more inductance.
Power planes do no harm in itself, but if they give you false sense of security of not requiring proper bypass caps, then they do hurt. Also if they increase your layer count, then they hurt in your pockets.
You wag your tongue fiercely, but you have never actually tested your ideas. Your hand waving of connecting the power plane to the pin being a bottle neck is not based on any technical analysis. You clearly fail to understand the nature of a transmission line. You are doing the same faulty sort of thinking that makes people talk about the loop impedance of a cap connected to a chip via the ground/power planes.
As I've said, these are not my ideas. This is from Lee Ritchey, who analyzed this in theory (correct theory), simulated it in a 3d field solver and tested it by building a board. He connected the cap next to the pin, and at several distances from the pin. There was virtually no difference in the voltage waveform at the pin, until the cap was something like 4 or 6 inches from the pin. A very clear and simple demonstration.
If you want to argue about this, perhaps you should take it up with Lee Ritchey. He is one of the very few "experts" who actually build circuits to verify his thinking. It took me a while to get my head wrapped around what he was saying in his class. Once I did, it all made sense. People tend to get some wrong perspective on problems like this, and let it take them in all directions.