If they could, they would read your mind too.
The Department of Justice is saying that a fingerprint is more like a key than a password I guess. Or alternatively that unlocking phones is search and not testimony.
The EFF seems to be primarily objecting on the grounds that a search of "all devices in the building" is too vague to be a correct warrant.
[1] http://www.uclalawreview.org/the-fifth-amendment-encryption-...
The self-incrimination clause of the fifth amendment is broadly interpreted as intended to dissuade the government from attempting to coerce confessions. Forcing someone to unlock their phone with a fingerprint caries none of the moral hazard of forcing them to testify.
All of that being said, I'd love for US society to recognize that a search encompassing a bunch of people's phones is vastly more intrusive (by virtue of the volume of data collected and network effects) than a search of a building that excludes computing devices, and for us to require a correspondingly higher burden of proof.
If you don't want anybody to be able to take your stuff, don't make it possible for somebody to take your stuff. A piece of paper saying something isn't permitted is not going to stop it happening.
It's no different, really, then that they can force you to press your fingers onto a sheet of paper for booking during an arrest, or to take a buccal swab.
What they apparently cannot do is force you to admit what if any finger of your would unlock the phone. Apparently some people use tricks like locking the phone with a knuckle or even the tip of their nose (that one sounds comical). Really though, it goes to show that the good old fashioned memorized password has not gone out of style. Any biometric or dongle-based authentication or encryption can be circumvented by legal process.
And in a civil matter, judges and parties have even more power. Ultimately, if a court is convinced that you know a password and are not properly invoking a 5th amendment privilege against criminal self-incrimination, you could be held in contempt (fined daily, or jailed) until you provided the password or the password-protected materials. At this point it could well become a battle of wills and proofs, which the contemnor may well lose.
That seems to me to be a very reasonable thing to say. It seems to me that we have plenty of mechanism in place to say "you have X, you can use it for Y, and not Z, because using it for Z violates someone's rights". As a super contrived strawman example, if your computer ever gets confiscated by law enforcement, while they may be permitted to search it, they can't just play Fallout 4 or mine bitcoins on it.
Another instance I think is similar in concept: juries are instructed to disregard things (i.e. pretend they don't have a piece of information for the purposes of a trial) all the time, when access to this information would be improper.
Relevant bits start at page 5 (III - LEGAL DISCUSSION).
and yet here they are as a matter of fact seeking "communicative evidence".