I think several points are being slightly overlooked:
1. I am not saying that a comparative form with no always and only means a simple negation of the comparative in the sense of no ...er than = as ...as. I am simply saying that it can imply this.
2. I am not saying that a comparative form in a negative utterance with not always and only implies an opposite comparative form, merely that it can.
3. English is a language. Languages do not always follow the rules of formal logic,
4. There are clearly situations in which there is a difference between no-negation and not-negation. I gave an example of this in post #6.
Having established a difference between no and not- negation with a noun, we can consider whether it is possible with a comparative structure.
1. Prague isn’t more beautiful than Paris.
2. Prague is no more beautiful than Paris.
In 1#, the (contracted) not negates the verb, and therefore the whole assertion. In #2, it is not clear whether no is to be read as referring to more alone, or to more beautiful. Both readings appear to be possible. In the case of the former, definitely, and the latter, perhaps, then it seems to me that there is an implication that Prague is as beautiful as Paris. It appears to be impossible to ‘prove’ this. All I can say is that in my own usage, and in that of others that I have encountered, this appears to be possible. I feel that #4 below is less likely to be heard than #3.
3. Prague isn’t more beautiful than Paris; in fact it’s rather an ugly city outside the Old Town.
4. ?Prague is no more beautiful than Paris; in fact it’s rather an ugly city outside the Old Town.
The situation with comparatives formed with –er is not so striking, but I feel that #6 is less likely to be heard than #5
5. I’m not taller than John; in fact, I am quite a bit shorter.
6. ?I’m no taller than John; in fact, I am quite a bit shorter.