Various things that I've heard include: The combination of Cybill Shepherd's and Bruce Willis' gigantic dueling egos, Cybill's pregnancy, Glenn Gordon Caron's nonsense, Bruce's post-Die Hard movie success, the mangling of Dave and Maddie getting together
Basically all of the above and more.
I do believe that even though Gordon Caron had previous experience it is my opinion that he had never had as much responsibilities on a TV show as he had on Moonlighting and his inexperience in managing stars-actors led to a lot of the off screen drama. Also the TV schedule of that era was just not right for him and his production team, they needed more time, they were always behind schedule which also had many negative repercussions on many aspects of the show.
I felt it had nothing to do with putting the characters together it was the stars of the show wanting to do other things
shareA lot of people stopped watching once the 'sexual tension' between the two leads disappeared when they finally began sleeping together late during season 3, the ratings simply never recovered from that point and I would say that was the #1 reason.
I would say Cybill's pregnancy-absence would come in second.
But as you mentioned it was a multitude of factors which all contributed.
There were also many delays during the show's production, I believe the show was too ambitious for the era it was produced and they had to air reruns quite often which also contributed to people tuning out... nowadays if this were produced for let's say a streaming platform they could just do 10 episodes a year and release them weekly or all at once... but I believe back then ABC was attempting for the show to produce +20 episodes x year (which it never did lol).