Of course you can encrypt things yourself, and I would imagine you could probably refuse to hand over the password under your 5th Amendment rights. Nothing's changed there.
I think the issue here is that someone else (Apple) has gone and set up an encrypted environment for you in such a way that actively prevents law enforcement from carrying out legal investigations with a warrant on an incredibly popular series of devices that they were capable of searching before. Let's face it - the number of people who are buying iPhones because they are now encrypted is miniscule. If you really wanted to encrypt all of your data, optional full disk encryption already existed on other phones. The problem the police have with it is that it's now set up by default, they can no longer access it when they do have a valid warrant and this extends to everyone instead of just the handful of criminals that would take extra steps to encrypt their data. John Q. Criminal didn't choose to encrypt his phone, Apple made that decision for him.