Suggestion: leave enough BTC to cover at least 1 set of fees when a user gets a new asset. It's a pretty poor experience to get an asset and find out that it can't really be transferred immediately. Fees for 1 transfer will improve usability, and after it is used, a message could be displayed that further transfers will require depositing more BTC.
Whom are you suggesting should leave the fee when a user gets a new asset? Or are you suggesting that a user should need to have twice the BTC dust at his address in order to create an asset, so that he'll also be able to send it in another transaction?
I was thinking the distributor. I don't know the details, but when an asset is distributed the very first time, a user gets BTC dust: if the dust was bigger so it included a fee, a user would be able to immediately transfer the asset.