In summary:
Why are so many airports missing? → We do not know.
How many airports are missing? → We do not know.
Are there also large, international, airports missing? → Yes.
Do we have to report missing airports to Zendesk? → Yes, and also add them to this topic if they are not yet mentioned: Missing Airports Sent to Zendesk
Will missing airports, reported to Zendesk and this topic, be added later → Maybe or maybe not. We do not know.
Will missing international airports be added in subsequent World Updates for this area? → Maybe in the future, maybe not. We do not know.
What can I do if I really want a missing airport? → Report (see above) and / or look for a third party add-on.