He's a .500 starter on a team that is dying to have a .500 starter hold down a start every 5th day. You've called him a 2 WAR pitcher, Doc, but he has not been the pitcher he was in Cincinnati - which is why St. Louis is happy to move him and free up salary even after having to throw some in. Of course, they have minor league arms who are ready to go and we have "straws." They've given us Leake as a #4 starter and Marco as a #6 just to clear the decks.
Leake is a groundball pitcher in a league with juiced baseballs giving flyball pitchers headaches, so that's useful. Seattle has a normally-good-fielding infield, which will also help. Moving to the AL won't help him as much, but he's still better than some other options (most of which the Ms have tried already). His hits-per-9 have ballooned in St. Louis, though. Perhaps that's defense, perhaps juiced balls also get through the infield faster, perhaps he's just catching too much of the plate with adequate-but-not-overpowering stuff.
The Cardinals paid for a 3-WAR pitcher who only gave them 1 WAR. The Mariners got the discount and are trying to pay for a 2-WAR pitcher they'll actually get. It should help stabilize the back of the rotation in the coming years, assuming he's able to stay as a rotation fixture. If Paxton can go 10 games over .500 and the rest of the rotation could just go .500, and the pen can blow just a handful of saves, teams can be fine.
Unfortunately the Mariners have had ONE starting pitcher with an FIP under 5 whose nickname is not tree-related: Andrew Albers. Other than his handful of innings and Paxton's once-again-injury-shortened campaign, the Mariners have had abominable starting pitching no matter who is on the mound. If Leake can post a number around his career mark near 4 for the next 2-3 years the Mariners should carry him around on a wicker chair like C-3PO in the Ewok village.
These Mariners have had a lot of average-ish hitters and one great one. They tried the same formula with the pitching staff but it's not working. Leake is part of the next campain of averageness and unlike Gallardo he might actually succeed.
With Seattle, the ability to be average is graded on a curve of greatness.