Your observation is backed up by modern neuroscience. Effective multitasking is largely a myth.
Obviously one can context switch, but every switch comes at a cost. That cost could be hidden by happiness boosts from not having to think about this difficult thing (=pain) and instead do something simpler that feels like lower hanging fruit and gives more immediate gratification (=reward). But the shower you mention is key and can't provide progress on multiple hard things at once. I agree that this is akin to a procrastination strategy and commend you for the analysis and self reflection.
Obviously one can context switch, but every switch comes at a cost. That cost could be hidden by happiness boosts from not having to think about this difficult thing (=pain) and instead do something simpler that feels like lower hanging fruit and gives more immediate gratification (=reward). But the shower you mention is key and can't provide progress on multiple hard things at once. I agree that this is akin to a procrastination strategy and commend you for the analysis and self reflection.