I am going to stand by my last sentence. Don't blame the grease YOU put on, blame the grease someone else OMITTED.
A spline should fit the hub within a few .0001's of an inch. Not .001, .0001. There should be virtually no play perceptible.
One of the sources of wear is called fretting corrosion. The spline wears as it transfers torque, because the teeth of the shaft bond to the teeth in the hub, then break away when the torque reverses. It is just a minute amount of bonding, microsopic. The wear appears as corrosion products. The wear is similar to that seen by gear teeth. If you look at a spline, it even looks like a gear, the shape is the same. Lubrication stops the spline from bonding, and prevents wear.
Once the wear has started, the play gets worse and worse as the loads seen by the splines get higher and the torque reversals more obvious. The fretting increases. It may get to the point where it isn't really fretting anymore, just plain wear as the hub slops around.
http://www.engineeringtalk.com/news/skf/skf162.html
http://www.hghouston.com/Technical%20FAQs/TFAQ106.html
I am not just making this up, as the links above prove.