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.
Well, あせ and いびき simply take the verb 掻く. It's just a matter of collocation.
https://en.wiktionary.org/wiki/%E3%81%8B%E3%81%8F
https://en.wiktionary.org/wiki/%E6%B1%97%E3%82%92%E6%8E%BB%E3%81%8F
There are more meanings to consider: https://jisho.org/search/*%E6%8E%BB%E3%81%8F As most of them are not listed in the entry for just 掻く I wonder why "to sweat" has made it. And I'm quite sleepy but I can't find any explanation for meaning like in 田をかく or 鰹節をかく or からしをかく which all don't seem too obscure.
We don't say 田をかく, and it usually doesn't make sense. If you use かく with 鰹節 and からし, they just sound 鰹節を欠く and からしを欠く, and I can't think of other way to say.
田を欠く？Not impossible but would be rare.
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.