Notice the "El Tapatio" hot sauce next to the shoyu (soy sauce). I don't usually use it because I can't handle spicy/hot, although I do like a teaspoon of the Vietnamese hot chili sauce, which now comes in squeeze bottles, in hot soup with udon.
I don't think "El Tapatio" is available in Japan. If it were, though, I wonder if it would be a popular condiment at ramen shops and other Japanese food restaurants. Part of me would say yes, because most Japanese women my mother's age I know, have it at their homes.
I also wonder if using "El Tapatio" or the popular Vietnamese hot sauce makes Japanese udon bowls less authentically Japanese. This brings up whether authenticity is really a food/cultural issue or an ethnic/biological issue.
I believe it's a fine line between the two. On the one hand, if the "El Tapatio" condiment was labeled in Japanese, I think Japanese people both in and outside Japan would believe the condiment to be an authentic Japanese food condiment.