No it does not. You literaly have much weaker characters in OP who have better haki mastery than much stronger characters. Who would be a better teacher in CoO Haki, Katakuri or BM? Hyogoro and Sentomaru have barrier haki, while BM and especially Kaidou don't seem to have it. Hyogoro even knew about the internal destruction haki, while Kaidou is stil shocked why he gets damaged...
The teacher in this case are way stronger than their students. It makes no differents if they are 50 times stronger than them or 100 times. They are not gonna go all out on them anyways and will apply only the force needed to make their pupil struggle - which is not their 100% anyway, so it makes no difference if Mihawk is stronger than Ivankov.
Read the manga, some things are so obvious you don't need any literal text to understand that.
This is simple logic lmao - explain to me how is this headcanon? We always see Sanji cook, Nami navigating/drawing maps, Franky doing stuff on the ship or improve himself, Brook playing music etc. Because it's their jobs on the ship. What job does Zoro have? Combatant. If you show all the SH's do their job, what would Zoro show us with such a job if there is no fight going on? Exactly train or sleep, because he doesn't do anything else.
So you are telling me Luffy's gears and Sanji's DJ came out of nowhere? Luffy even said he wanted to test a new technique before getting to EL. But did we ever saw him train? No. Same goes for Sanji, it was not a random ability he randomly tapped into, he knew exactly how to activate and use it, which just proofs they trained for it.