The requirement to remember the churban is incumbent upon Jews every day (top of page 2) and is especially important at times of joy. Aside from the practices of leaving a wall unfinished/unpainted, or leaving food aside, or not listening to music, there are liturgical changes which reflect an awareness.
Though it might not be the primary reason, I would think that including a mention of the exile in Megillat Esther (and all the moreso, using the tune of Eicha when reading it) would be a reminder during a joyful holiday. Breaking a plate and/or glass as a reminder during the simcha of a wedding is also a reminder. Saying "al naharot bavel" reminds us on weekdays. And on Yom Tov and rosh chodesh shechal b'shabbat we say a line in musaf which explicitly recalls that our sins brought forth the destruction of the temple which prevents our offering korbanot, so even on those joyous days, we recall the churban.
But on Shabbat, and on a rosh chodesh which falls on a weekday, that sentiment is missing from Musaf. In both cases, we do use the future tense and indicate a hope that we will offer korbanot in the future, but the text lacks the specific statement which would recall the churban.
I understand that one could say that the other food/furnishing practices still exist on those days, but those remembrances would also be active on Yom Tov, so why is there a need to recall the churban explicitly in the davening on those days?
Bottom line, why does the text for Musaf on Shabbat and on R"C (two days of simcha) not have the zecher of the churban while the zecher is there on Yom Tov and Shabbat-R"C?