In AM you have a waveform typically formed like this:
Rectification chops off the negative portion of that signal, thus:
Filtering then removes the high frequency component:
A capacitor then removes the DC offset:
Nowhere in that does the frequency change.
Even if you were to use full-wave rectification, only the frequency of the carrier would change - the modulated signal frequency will be just the same as it was.
In the image you provided in your comments:
The modulated signal is modulated twice - once on the positive axis, and once on the negative axis. This is the same as the top image above. However, the modulating signal has an amplitude that crosses the zero axis, so you actually end up with two signals crossing over each other, like this:
When you then rectify and filter that waveform you get just the positive portions of both waves:
With pure audio modulation (modulating two audio signals together) this can be desirable as it produces very noticeable affects and artefacts (you would never typically demodulate this signal, it would be the finished audio product in its own right). In RF modulation though it's not wanted, so the incoming signal should have an amplitude of no more than 50% of the carrier frequency, and be off-set to half-way up (and down) the carrier wave so the two sides of the wave don't cross over.
A picture is worth a thousand words.
The carrier and audio modulating signals are simply added but do not form a modulated signal.
The diode rectifies this signal forming a crudely modulated signal which contains a DC component, low frequency component and high frequency component.
The inductor acts as a low impedance for the low frequency component and high impedance for the high frequency.
The capacitor blocks the DC component but passes the high frequency AC signal
The tuned LC circuit filters out all but the the desired AM signal.
Best Answer
Consider that in general a load is measured at some point in a network, and can be defined as load Z = V/I at that point in the network.
In an efficient amplifier, we want the load seen by the power devices to be such that the devices are as close to saturation as possible on a moment by moment basis, which if you think about it is saying that the drain load impedance should be inversely proportional to power output.
In a classical power amp the drain impedance is fixed at a level that is low enough to support whatever the maximum power the thing is capable of, which is fine for a constant power mode, but horrible for anything with a significant AM component (Like say just about any efficient modulation scheme) as the input power falls as only the square root of the output power backoff (This is an inherent property of a fixed drain impedance/fixed power rail design). Doherty can be thought of as using the peaking amplifier to lower the drain impedance of the carrier amplifier during modulation peaks this allowing the main amp to run a higher native drain impedance and be more efficient over the vast majority of the time when peak output is not required.
Due to the 1/4 wave phase shift, they are inherently narrow band devices, but IIRC the first ones were indeed built for ~100kHz long wave service by Continental transmitters using valves as the active devices. A 90 degree phase shift does not need to be a transmission line, you can do it using a lumped element hybrid made from a coupled inductor and two capacitors, still narrow band, but workable down well into the audio band if you really wanted to. There are easier ways down that close to DC with modern parts, PWM with a GAN switch will make very efficient power up to at least the medium wave region without the narrow bandwidth of the Doherty designs.