Is it really that important for Ethereum to be anonymous, and could it be enforced only on a per transaction basis (meaning each transaction in ethereum can be anonymous or not at the discretion of the sender)?

From a business perspective anonymous is not necessarily a good thing. Sometimes having funds and transactions available for the public to see can provide legitimacy. For example if you buy a product online and pay with some digital currency, that transaction serves as your receipt. If the transaction is anonymous then your receipt is worthless as it proves nothing. But if the receiver's address is known , and you can verify ownership of the sending address, the transaction is forever recorded on the blockchain as your receipt. Anonymity can be useful but it can also be a detriment depending on who you are.

If Ethereum is designed to be a platform for crypto based services then anonymity should be a choice, based on the needs of the service. Just my 2 cents.