I noticed that only possession traditions get Task spirits. Is this intentional? Is there any way to get a Task spirit with the Materialization power?

Well, one way would be to simply create a materialization tradition that summons task spirits.
It's not like the traditions listed in the rulebook and in Streetmagic are the only traditions that exist in the SR-world.

All it would take would be a custom tradition. Note that I can't see anything particularly broken about a task spirit that can materialise, plus they have amongst the poorest physical stats of the various spirit types.

Also remember that physical stats for spirits only ever matter when materialising. If it was intended that task spirits should not be able to materialise, why did they bother giving them physical stat mods?