Right, these flights of stairs are generally self supporting, in that even without the framing that the plasterboard fits to the stair will be OK in use.
The framing is simply there to fix the plasterboard [or what ever] to, having said that, the framing definitely does give a load of support to the unsupported stair stringer, the structure will not "flex" as much as an unsupported stair, there will be a lot less cracking of the joint between the wall and the stringer nearest to the wall.
The underside of such stairs tends to be [slightly] unsightly so tends to be covered and framed by something. Especially the area nearest to the ground floor.
Thanks lads! Sounds good! I’ll be building studwork for understairs storage that would replace any load bearing anyway. Just wanted to be sure it won’t cause any issues if I remove these 2x2s in the meantime