When a budget speaker is preferred to a high end one...

The video / audio comparison is flawed and similar. The similarity is just like audio, once you reach a certain resolution (assuming equal viewing distance), then there is no improvement. Where it breaks down is that increased video resolution means increased bandwidth. We often don't like increase bandwidth because we can see flaws, i.e. poor skin complexion, that may be hidden in a lower bandwidth image. For audio, we tend not to dislike full bandwidth, though in similar fashion, if there is excessive high frequency energy, i.e. cymbal crashes, we may prefer a subdued version to the real one. A cheap speaker versus an expensive one does not work that way. I can guy a cheap speaker that easily does 20KHz without dropoff.

Distortion? No one likes distortion in video, whether optical or at the signal level. Think of blocking artifacts from compression. That is distortion. We don't like it because it is unnatural. Unless we are listening to music that has inherent distortion, electric guitar and other things were we associate distortion as art, what evidence is there we like distortion??  I looked. I cannot find any. More phile lore. I may have to trademark that "Philelore".   No, a distorted speaker just sounds bad. It never makes a bad recording sound good. It usually makes it sound worse.  I cannot say I have ever enjoyed a bad recording more on a cheap speaker or system. I have enjoyed a bad recording more by using an equalizer. A more expensive speaker is not a gurantee of better frequency response once it is in your room.

i must comment that one member here misunderstood my meaning, i was not talking about speakers which put out bona-fide distortion, i was talking about less-revealing speakers esp. in the treble range. many poor recordings have obnoxiousness in the treble range, and a less-revealing speaker will tend to blunt or obscure those treble failings. ONLY in that limited respect do such speakers "sound better" on the vast universe of mediocre recordings out there [like the ones i have found at flea markets and garage sales and goodwill stores since the 70s], only a minority of recordings are "audiophile-approved" and i suspect this commenter is not familiar with the mediocre [worn or poorly made] recordings i have and like a lot, as well as my experience in listening to those particular recordings with a 50 year old set of inexpensive speakers in a non-audiophile-approved room.  similarly, a speaker that images in a substandard way will not as eagerly remind its listener of a flawed/poorly made stereo recording, it will tend to make lopsided stereo mixes less obvious. these recordings NEVER sounded better to my ears on fancier equipment, their flaws were made too obvious to me. 

Nope, I understood you and do not agree. Less revealing does not blunt anything. it will make it worse. That is called distortion. If there is a shelving in the frequency response that has nothing to do with cost, that is a design decision. Cheap speakers can have as much high frequency extension as an expensive one in audible frequencies.

What you describe is Philelore. Not real, but often repeated. You simply have a speaker with a shelved frequency response. It has nothing to do with more distortion (or less). A distorting speaker will make a distorted poor recording that much worse.

I think I am about to test the OP’s theory out soon with this speaker.

SIERRA-2EX PAIR - Ascend Acoustics

I was planning to replace my 10-year-old KEF LS50’s with a bookshelf speaker around $10K USD. However, the speaker listed above has a driver that I love on my headphones, and I have gear that would work with that driver on bookshelf’s. It is not a cost issue but a sonic issue on this choice.

I checked on images of Harbeth crossovers and was shocked. I dont care about the quality of the parts so much as the design itself. Check out some of the crossovers on Thiel speakers.