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To put it bluntly, to the best of my minimal understanding, expensive headphone amplifiers seem to be a preposterous rip-off.
Yes and no. A whole lot of expensive hifi kit is a rip-off but you need to differentiate between "good" kit and "expensive" kit. There is a very loose connection between price and quality with hifi kit, especially with real top-end stuff.
On the other hand, headphones are quite hard loads for an amp to drive which means that you need a good amp to drive them properly. Basically you need an amp which can drive a headphone type load while remaining linear and not clipping (at all).
Basically, an amplifier tries to feed a voltage waveform to a load (speaker or phones) which causes a current to flow. When the current gets to high for the amp to supply, the voltage drops and the sound is distorted. A good amplifier will not allow this to happen, because it is designed to be able to source enough current so it can provide a clean waveform right up to maximum volume.
Another source of distortion is introduced when the amplifier output voltage exceeds the supply voltage (clipping). This is purely a matter of trying to supply more volume than is available. A good amp should never be driven into clipping without severe provocation (enough to deafen you or kill your headphones).
Basically, before you strike out too strongly against headphone amps, understand how they work, what they do and what benefits they have for your sound. Listen to a few and see if you hear a difference. And it needn't be very expensive - you will be surprised at how cheap it could be to build or buy an amp which could greatly improve your sound.
Good headphone amps are not a rip-off. Expensive headphone amps might be.
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sound processor inrests me which makes headphones sound like speakers not like left and right
If you are using a computer as a source this is probably best done in the digital domain. It has been discussed plenty of times around here before - no need to shell out hard earned cash for something you can get for free. I have a personal belief that analog signal processing is evil, but on the other hand the circuit for this kind of cross-feed would be very simple.
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But since we're plugging this after the headphone jack, we're feeding this expensive amp with the output of the other, supposedly not-so-good amp. In this case, isn't the damage already done?
No, not really. The low quality amp will deteriorate the sound to some extent, but most amps perform much better into a multi kiloohm load (like another amp) than a few ohms or hundreds of ohms load, like a set of headphones.