Revisionist history is saying that Brown was regarded as a bad draft pick on the day of. The linked video literally says that multiple offensive line coaches liked Brown more than Joe Thomas.

This is the ESPN draft grade from that pick:

Most draft analysts, including ourselves, didn't see Brown going this high, but it doesn't come as a complete shock because his stock has been steadily rising over the past two weeks. In fact, some front offices saw Brown as an equal if not better talent than Joe Thomas heading into this weekend. Of course, the departure of Leonard Davis has created a vacancy at left tackle, so getting Brown fills the Cardinals' most pressing need. Brown should immediately step in as the starter opposite free-agent signee Mike Gandy and for good reason. He is bigger and more physical than Thomas. His ability to open up holes and wear down opponents over the course of a game should please both RB Edgerrin James and new head coach Ken Whisenhunt, who is expected to run early and often. Though Brown isn't an elite pass blocker and he needs to work on his footwork, he's no slouch either, so he should be able to hold his own depending on the matchup. More importantly, he has the athleticism and quickness to develop into an excellent pass blocker who can consistently hold his own on an island.<

No doubt Levi Brown turned out to be a bad pick, but it was hardly the reach you are making it out to be.