Why does Cardano need ETC? How can this coin be profitable for Cardano?

It is in Cardano's best interest to be interoperable with as many systems as possible for transaction volume to flow from one system into another system.

Cardano is not only a service provider for users and Dapp developer but also other cryptocurrencies. Charles gave the example, that if Litecoin decided that they also want to offer Smart Contracts, they can move their LTC to Cardano, and do their work on Cardano that is not able to be done on Litecoin. That way every ADA holder, service provider, stake pool operator, and delegator, is benefiting from the economic activity, made by Litecoin.