Have you try it yourself? I think you're just make an assumption since it's possible to get an airdrop by using exchange wallet.
You are wrong. You can use an exchange address if you like, but if the airdrop got lost and the exchange is not willing to give you the airdrop coin after you have stressed yourself complaining to them and tired, you will learn your lesson of not your private key not your coin.
The reason why they're ask everyone to use their own wallet instead of exchange because they don't want the airdrop participants suddenly dump their token.
You are wrong again, if the coin becomes tradable, you can move it to any exchange that list it, for you to trade it to other coins. But still not all exchanges will list it.
Also when they use their own wallet, the participants will take a part of the network since they need to send their token to the exchange.
You are wrong again and again and what you post is not making any sense at all. What kind of network they want airdrop participants to take part in? For transaction? Who cares? Even a project is successful without any airdrop.
