File sharing is still the most important function of a client portal. Sending sensitive files through unencrypted email is dangerous and even illegal in some areas.
Outside of standard email you have limited options, all of which have obvious drawbacks. Not everyone has access to a fax machine, and quality is often poor. Standard mail is far too slow. Encrypted email is expensive and only useful for a single task.
Modern client portals make file sharing as simple as posting a picture to Facebook, and keep your data more secure than it is on your hard drive.