As the domestic court presupposed morality, public accusation did also ; and for that reason these two things disappeared along with it, and ended with the republic. 
The institution of the perpetual questions, in other words, the division of jurisdiction among the prætors, and the more and more prevalent custom that these prætors should themselves judge all causes,  reduced the use of the domestic court : this appears from the surprise of historians, who consider as singular acts and as a renewal of the old practice the cases Tiberius had this tribunal decide.
The establishment of the monarchy and the change in morality also brought an end to public accusation. One might fear lest a dishonest man provoked by his wife’s disdain, indignant at her refusals, exasperated even by her virtue, conceive the design of being done with her. The Julian Law decreed that one could accuse a woman of adultery only after accusing her husband of facilitating her misconduct, which much restrained such accusation and all but eliminated it. 
Sixtus V seemed to wish to re-institute public accusation.  But it takes little reflection to see that this law, in a monarchy like his, was even more out of place than in any other.