Comment by DiogenesKynikos

I agree on not over-intellectualizing the tones.

I've seen people struggle to pronounce a word when I explicitly tell them what tones it contains, but then pronounce it perfectly when I ask them to just imitate me.

But I disagree about accents. One of the major flaws in most foreign language education, in my opinion, is that pronunciation is not emphasized heavily enough at the beginning. Being able to pronounce the basic sounds correctly has a huge impact on how native speakers perceive your language skills, even if you're not very advanced in the language.