So your title and your post ask two different questions:
1. Why are monks tied to Pandaren culture?
2. Why can't Zandalari be monks?
The former has been answered pretty extensively by Blizzard over the years. The monk class represented is a product of Pandaren culture and training--all associated techniques, symbols, etc., are all therefore Pandaren.
The latter--meh, I agree. I don't feel so emotionally angry about it since it doesn't impact me--I don't play monks--but if every other race can be trained to be a monk lore-wise after the faction incursion on their land, the same logic would have to be applied to Allied Races, too. If it's a question of time, non-Pandarens were in the same boat when the mists parted.