(Illogical comparison, change of tense are 2 kinds that I know when we need to add the verb behind the sentence again)
I don't know what you mean by "illogical comparison". Perhaps you can clarify.
In addition, there are sentences that are ambiguous without the helping verb.
E.g.,
Tom has known Sarah longer than Carlos.
As written, this sentence has two possible interpretations:
1/ Tom and Carlos both know Sarah, but Tom met her first.
2/ Tom knows both Sarah, whom he met first, and Carlos, whom he met later.
If you add "has"...
Tom has known Sarah longer than Carlos has.
then the meaning is unambiguously #1.