That's not what happens with real speakers. This is what happens with real speakers, it will vary with load but this is what I got from an aiyima a07. I tested three a07's and got different rising responses towards the top end with each one but similar behavior of things starting to rise around 5khz (just the tweeter here and it's passive network, c note speaker).
While I'm not a big fan of the youtuber Andrew Robinson, he put out a video documenting the same problem, but he wasn't sure what the cause was, just that he was getting totally different HF responses with different amplifiers.
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Same tweeter with amp that doesn't have load dependency (had woofer connected for this one, can ignore below 2k,). This seems like a good opportunity to market "non-load dependant" amplifiers from the budget amp makers. I've had people tell me it's just these speakers that an outlier, nope found plenty of commercial offerings with very similar impedence charts, like kef q150. Most people are pairing these speakers with cheap amps, I wonder how many complaints about brightness are because of this issue. I will continue to rate any amplifier with this issue as poor as I don't consider it acceptable and it is a design flaw in my eyes.
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I measured my different apeakers with different amps, never experienced what Robinson did. He seems to be a 100% subjectivist so I am very surprise he would bother measuring FR or anything, so I don't know what to say about his measurements, at least not until I watch that video. In theory, as long as the amps have low enough output impedance, such as damper factor of between 50 and higher, even 50 vs 1000, in the audio band, it should not affect the anechoic FR of a speaker by more than a couple dB. But then, people like Robinson will never trust theories, specs and measurement more than what he thinks he heard. He obviously is the typical trust the ears only type.