As a North American who enjoys discussing taboo subjects clinically and honestly, and in the interest of cultural understanding, I would explain it as:
Cleanliness standards for the hands are much higher than for the rectum area. For hands, not just water but soap is expected, after any work with biologically-suspect materials or surfaces (raw foods, places of illness, bathroom visits).
But for "down below," the paper-wipe is considered sufficient, with usual assumptions about clothing, bathing schedule, etc. The paper enables wiping until there's no trace (on the white paper) of any feces. The seated toilet (less common in other regions) helped spread open the rear cheeks; after standing any surfaces that were only-paper-wiped seem very nearly 'retracted' so as to not even be in contact with underwear. Within 12-24 hours, a full-body bathe and freshly-cleaned clothes are likely.
Still, those with predictable bowel movements may time them so they immediately precede a daily shower. In many bathrooms the sink is close enough to allow wetting toilet paper for part of the cleanup, and prepackaged moistened wipes are rising in popularity, and have long been used for messy-baby-cleanup.
Turning things around and looking at rinse-cultures, I'm probably not alone among North Americans in wondering:
(1) Doesn't the spray get droplets of feces-water mix everywhere? (Supposedly ideal bathroom hygiene is to close the toilet lid before flushing, to avoid sending a mist of toilet water into the air. Any forced-water rinsing seems to guarantee a mixed-mist reaches everywhere, including parts of the buttocks and legs far from the rectum that are never contaminated by paper-wiping.)
(2) Short of absolutely drenching yourself with multiple power rinses, how do you know you're "done" - that none of the remaining dampness is still fecal-contaminated water? (White paper provides a visual completion indicator.)
(3) My very rough impression is that fecally-transmitted diseases (typhoid, hepatitis, cholera, anything diarrhea-causing, etc.) are more prevalent in rinse-cultures. Are you sure that "a lot of South Asian countries" should be the "ideal way to wash" model, as opposed to the other way around? (North American practice would change very fast if there were evidence paper-wiping was insufficient to protect health.)