For multiple reasons, but here's one that strikes close to home: not every person who you may wish to have access to information contained in those records will have it via the health care system.

E.g., I need a personal trainer to help me work around my back problems. It's useful to be able to answer his/her questions by referencing my records, instead of vague shrugging about some random disc.

Another e.g.: my aunt does a good job of sharing family medical records so that we know who in our past had conditions that may be relevant to our healthcare as well.