Acharey Mos 120 words, but why did they die?

Shabtai Tzvi, the infamous false Messiah, retained loyal followers, even after he converted to Islam.

The sons of Aharon who were executed by HKBH, were great people who lived holy lifestyles; presumably they had [many] followers.

Chazal accuse them of –

being impatient to become the leaders of the nation
believing their leadership would be superior to that of Moshe and Aharon
defying the authority of Moshe Rabbenu
usurping their father’s privilege of burning incense
serving in the Mishkan whilst under the influence
believing no women were worthy of them
Were they too Frum?
Were they too influential, that there was no choice but to remove them from the community?