It seems you are attempting to perform the projection painting technique in Texture Paint mode, which is available in Sculpt mode and not Texture mode in Blender.

However, there is a way to achieve consistent and non-stretched texture painting on a cube. By utilizing UV mapping, you can unwrap the cube's faces and directly apply the brush strokes on the UV map.

By painting directly on the UV map, the textures will be accurately applied to the cube's faces without stretching or distortion. However, please note that this process may have its own minor flaws.

Yes, in texture painting mode, the brush strokes do not maintain the perspective of the surface when painting from different angles. However, in sculpting mode, the brush cursor adjusts to the surface of the model and considers the perspective, resulting in more intuitive sculpting interactions.

However, there is a way to achieve consistent and non-stretched texture painting on a cube. By utilizing UV mapping, you can unwrap the cube's faces and directly apply the brush strokes on the UV map.

By painting directly on the UV map, the textures will be accurately applied to the cube's faces without stretching or distortion. However, please note that this process may have its own minor flaws.