The name Doeg means “worry”, and we can suggest that Dovid wasn’t Machshiv the Torah of Doeg HaEdomi since it was devoid of Zemiros. (A worrier doesn’t sing so fast and without: סִ יפוּק הַ נֶ פֶ ש satisfaction in life, people do evil). הַנֶחֱמָּדִ ים מִזָּהָּב וּמִפַז רָּב וּמְתוּקִים מִדְבַש וְנֹפֶת צוּפִים תהלים יט יא Torah is also compared to the preciousness of gold and the sweetness of honey. We can suggest that Dovid was especially extreme in the music and sweetness of learning Torah, since he was a fiery: אַדְמוֹנִי ש"א טז יב flaming red head, with a Yetzer Hara like Eisav HaRasha, and the more negative fire, the more you have to go extreme with positive fire and extra Simcha. (Besides, Chazal say that his Neshama was created from the music of the Kisei HaKavod.)
Dovid was also extreme in his dancing in honor of the Torah, and his wife Michal bas Shaul was against this. Perhaps this is why only Malchus Bais Dovid were allowed to sit in the: עַ זָּ רָּ ה courtyard of the Bais Hamikdash (Gemara) since they had unusual respect for Hashem, even to be M'vazeh themselves; therefore they may sit in Hashem’s house. But other kings like Shaul, who weren’t so extreme, since their own Kavod was a factor, may not sit in the: עַ זָּ רָּ ה courtyard of the Bais Hamikdash.
