Because driving is framed as a privilege and not a right, and by partaking in that privilege you waive and right to refuse a sobriety test. (For bicyclists with no driver's license? That's an interesting question.)

The issue (at least as I see it here) is more about due process than the right to travel. Even if there were a right to travel, you could legally be denied that right for legitimate cases like parole or bail. But those cases mean you have your day in court.