Ebbin getting fired because Bounce didn't sell well could have been a reason - but on the other hand it's not his fault that the band didn't come up with hit material for the album. Without Max Martin, they probably wouldn't have had a hit on Crush either. Well, that's how it works everywhere. When a football team doesn't deliver, the coach is the first one to get sacked as well.

When Shanks came on board, they had a hit with Who Says You Can't Go Home and the following album was their first one to launch at number one if I remember correctly. That might've been a reason for him to stay.

Shanks definitely gets more hate than necessary amongst fans, but him being there is at least very closely connected to the point when it all started to go wrong with the band.
At that time, they were still trying to be hip and chasing hits. Shanks' sound was something they deemed to be current and I'm sure the band was absolutely fine with that. But the problem was that Shanks took that "wall of sound" to a new level and while they've had utilized loops and samples on the Bounce tour, they now needed more musicians to replicate the songs with multiple layers live. Jon's chance to go for his little own E-street band by taking Bobby and Jeff on tour with them.
But having Bobby as a permanent and Shanks taking over more and more control of the song production (also by doing tons of basic guitar parts) probably contributed to Richie feeling more disconnected with the brand that was Bon Jovi. We all know how huge Richie's ego is and in the long run, it surely pissed him off.

What I blame Shanks mostly for is that his way of producing songs has really watered down the quality of the songs. In fact, the songwriting hasn't changed too much over the course of the band's career. But since they've abandoned doing demos and all basic tracks are laid down by Jon, Shanks and a drum computer, there isn't much room for a song to develop. If someone like Tico and David only add their parts, they can put in a certain fill or vibe, but a song that's basically finished can only benefit so much from that. Dynamically, it can only evolve by them all being in a room and working on the songs. Remember that a song like Something For The Pain was re-done about 12 times? That's why it sounds different to anything. It developped and became something unique. Nowadays that's impossible.
I like the "New Year's Day" story, but it also brutally shows how stale the production process had become in the decade leading up that.
I'm sure that, at first, the band members were satisfied with that kind of production because of the frantic pace that the band used to have in terms of releases in the early 2000's. Have A Nice Day was practically done at the same time the stuff for the Box Set was done and re-worked. They surely welcomed that change of pace that this approach brought and then settled into it over the years.
And someone also brought up Jon's voice. I think that's a major factor these days as well. Not that only Shanks can hide it, probably any accomplished producer could do so. But I truly think that Jon is aware of how bad he sounds and might be embarassed to go into the studio with someone different.