I think it's because No Kings has little to offer young people.
Young people want economic mobility, quality public education, and a sane foreign policy including ending the genocide. No Kings protests tend to shy away from these subjects.
In fact, the No Kings protest is somewhat unique in that it does not have any specific demands at all. It has a focus on defending democracy and criticism of Trump, which are valid, but the main thrust is that older liberals want to go back to the pre-Trump era.
The pre-Trump era was great for these older liberals- it was their golden era- but younger generations do not look back so fondly. Millennials remember this era as a time of economic hardship; Gen Z are too young to remember the positivity of the late 90s/early 2000s.
The youthful political energy is with the DSA at the current moment. "No Kings" and DSA agree on many things, but there is also deep disagreement on many serious issues.