Yes, it is too confusing to try to learn the difference
No, we should learn correctly no matter how hard it is
I know that many people are learning English as a second language on this site so it may be difficult for them to distinguish the difference between a proverb and an idiom. But "a penny saved is a penny earned" is unquestionably a proverb because it says exactly what it means using only a bit of metaphor in the process whereas a "green thumb" is an idiom precisely because the meaning of that phrase has nothing to do with "green" or "thumb".
Aren't you doing ESL learners a disservice by teaching them incorrectly? Yes, it might be easier for them to learn the phrases in beginning, but later they will have to unlearn all the incorrectly labeled proverbs when they want to start becoming proficient with the language.