I have done this drive three times (LA to Zion/Bryce), most recent on September of last year, and there were no checkpoints at all. The last drive was actually till Arches and my brother-in-law (undocumented) went with us. He just did not help me with the drive for the little portion of the I-15 that goes through Arizona. He helped me with the drive within Utah. In February, I drove from LA to Four Corners, then to Santa Fe and Albuquerque, NM and there were no checkpoints in Arizona. If you enjoy road trips like I do, go ahead without any fears, just drive safely.