I think I've found some materials that give a rather different meaning for this pattern: it seems that they have the same tone for both parts of the sentence, for example: 白髪は普通増えこそすれ、減ることはない。(Normally grey hair never decreases, only increases) and 君のやったことは、ほめられこそすれ非難されるものではない。(What you've done is praiseworthy, and not something to be criticized)
I have finally gotten a chance to talk to a Japanese teacher regarding this, and her explanation aligns with what you said, and noted that while the second half of the sentence is always a negation, it is not necessarily a bad statement.
