I think the pain also comes more with surprise. The first time my sensei did nikyo on me (I think my second or third class) I could barely see straight. I also think this surprise is helpful in a fight. Someone throws a punch at Little Joe Aikidoka, they expect it to be blocked and countered, in which they can counter. Few attackers expect being thrown off balance and slammed to the ground (or given a nikyo, ude-osae, or something equally unpleasent).
"Aikido is non-resistance. As it does not resist, it is always victorious."