You may need new bearings and cones if you put some miles on the bike with the axle that tight. The skewer tightens it even more.

The roughness isn't the issue. A lot of bikes feel lumpy. the issue is that you shouldn't feel it while the quick release is removed.

If the bearings are shot, you will find some pitting on the cones. if so, replace cones and balls, if the cups in the hub don't also have pits. if so, there's not much you can do except replace the wheel.

Pits indicate fatigue, so even if they are slight, it will get worse real quick if you reuse the parts.