But I like the move for at least one reason: It shows the Saints have a plan for trying to fix their front seven, which is their most glaring weakness.
The reason the move is a bit of a head-scratcher is because the Saints already have a promising young middle linebacker in Stephone Anthony, the first-round draft pick who started every game last season and called the defensive signals as a rookie. He ranked 20th in the NFL with 112 tackles.
However, the Saints made it a top priority this offseason to bring in an experienced veteran "quarterback of the defense" type. Laurinaitis was the first guy they had for a visit in February after he was released by the Los Angeles Rams, though they kicked the tires on a few other options, as well.
Perhaps the Saints weren't pleased with the way Anthony was lining guys up or making adjustments -- which is entirely possible, considering how badly they struggled on defense in 2015, particularly when it came to pass coverage in the middle of the field.
Maybe the alignment and assignment stuff -- or just leadership, in general -- was a bigger factor than talent alone.
Or perhaps the Saints just want to free up Anthony to use more of his athleticism and instincts without the burden of running the defense. Whether that will include a move to the strongside linebacker position or even a possible switch to some 3-4 alignments remains to be seen.
Regardless, this is the first bold move the Saints have made so far this offseason toward improving a defense that shattered NFL records in 2015 for most touchdown passes allowed in a season (45) and highest opponents' quarterback rating (116.1).
The details of Laurinaitis' contract haven't yet been released. He likely won't break the bank -- especially considering the Saints had less than $3 million in salary-cap space as of Wednesday.
Laurinaitis, 29, has some attractive qualities, including the fact that he has started all 112 games in his seven-year career, ranks first in the NFL with 7,187 defensive snaps since 2009 and leaves the Rams as their all-time leading tackler, with at least 109 in each of his seven seasons.
Of course, another way to look at that is the 6-foot-2, 248-pounder has an awful lot of wear on the tires. He battled through a significant elbow injury last season, and his 109 tackles in both 2014 and 2015 tied for his career low.
Laurinaitis is a solid all-around player, with 16.5 sacks and 10 interceptions in his career, but he's not a dynamic athlete. And the biggest knock of all on him is the fact that the Rams just let him go. He's their version of recently released Saints veterans Marques Colston and Jahri Evans.
Still, if the Saints were seeking a quarterback for their defense, they got an excellent one in Laurinaitis, who should offer a boost both on and off the field.
And few units in the NFL could use a boost more than the Saints' front seven.