When making an interaction diagram - the upper bound for pure axial load, once you account for phi, 0.8 and 0.85 factors comes out to around 0.44*f'c. But typically you need to account for minimum eccentricity which causes some moment - and the length of wall you think you can distribute this point load over. Maybe residential loads are typically low enough that this doesn't matter too much - not really my realm.
Load in what direction? vertical up? vertical down? lateral? shear along the wall?
How is the load applied? in reality there is no such thing as a pure point load, there must be some sort of connection or bearing plate.
Compression could be critical if the load is high enough.
Saying the wall has no capacity is very conservative. Typically, residential foundation walls are considered pinned at the top and bottom (whether that's actually justified depends on the details). The capacity needs to be checked in accordance with ACI 318 CH 14 which a structural engineer can easily do.
No one is saying that! The description of this wall did not indicate that the top was laterally braced, so it may be a cantilevered wall. It was described as unreinforced, 10" thick and 8' tall on a 24" continuous footing. If so, the top is free and the bottom is fixed by a flimsy strip footing with no dowels into the wall to resist moment due to wind or seismic forces.
No engineer who wants to remain an engineer would agree that such a wall is capable of supporting an HSS column with a 25k load.
If the top of wall is laterally supported by a floor system, that makes a huge difference, but we were not told that. I do not infer conditions not provided by the OP. A simple sketch could have cleared that up.