Without the ability to pay for these services anonymously, you would be forced to reveal your true identity in order to maintain your pseudonym.
A situation which clearly makes no sense, and one with potentially dangerous ramifications.
Doing that on the internet is like flashing large stacks of cash in a dark back alley. A criminal might see how much you have, and decide to come after it.
Distributing your wealth between several wallets and using a different address for each transaction is a common practice that prevents others from knowing how much Bitcoin you have.
True pseudonymity against a resourceful adversary is very difficult to achieve.
Bitcoin is by default a transparent system, in which every piece of information is available to the public.
As such, every Bitcoin user requires some level of protection.
Privacy in traditional banking is guaranteed by the institutions that make up the system, such as banks, credit card companies, and governments.
They (try to) ensure that your bank balance stays a secret.