I don't think it has to be "pure". Ethereum is not purely functional. However, it helps if it has a significant functional use.

It does seem that the best-advised projects avoid listing pre-sale tokens on an exchange. This hasn't stopped them from raising loads of money for their respective foundations, in exchange for cold wallets or invite codes.

The devil is always in the details. Very few people have the relevant experience to advise in this field with any confidence. I do not claim to be one of them.