Dear @Layne deCooman
Thank you for your explanation
Your explanation is more understandable for me (as not a native speaker)
I agree with you, and understand where I was wrong,
But there is a point I don't understand --- that you mentioned [because with the "... market, BUT they are the best quality." would then argues with both points slightly]
2. In my opinion, the meanings of "not the cheapest" and "not the most expensive" are very close.
The ranges are large, both of them can mean cheap, neutral price, expensive, and any kinds of prices, but only not the highest or the lowest price.
3. We say "the most expensive, and with the best quality."
=> They are not the most expensive, but they are the best quality.
For me, it is reasonable and with no argument.
If there is anything wrong in my opinion, please help to correct it. Thank you for your attention.