Is 掻く used on its own to mean "snore"? If I google image search, every single result is of someone scratching. It seems that you need to explicitly say イビキを~ for it to mean "snore". Goo dictionary lists both sweat and snore as sub-examples of one meaning: ７ あまり好ましくないものを表面にだす。Like, "to bring something undesirable to the surface", but it seems you still have explicitly use イビキを~. Maybe the jisho entry could be organised like that? I dunno, not my call, I'm not advanced enough to say.
It's probably related to common usage. Japanese tends to omit subject/object when speaking, so when a phrase was repeated so many time without the subject/object, the meaning eventually sticks to the verb too. The phrase 運がつく/ついている got the same treatment. Nowadays they just say ついている without the 運 to mean "lucky".
いびき is probably not so common to warranted the same treatment.
Synonym for 'snore'
Hi. The expression イビキをかく can use 掻く, just like 汗をかく. I think having a definition of this word as 'to snore' is warranted, since 'to sweat' IS here.