Plenty of people aren’t going to like the concept of anyone being Batman except Bruce (and Terry in Batman Beyond circumstances). Besides the edges to Jace are what make him interesting. Sand those off and he’ll be boring, if you want a “nice” Fox family member who is on good terms with Bruce, that’s Luke’s lane. Jace needs to be on the outs with the Gotham Batfamily to work.
The problem with Jace being part of the Bruce Batfamily is:
1. That family is too big. Already you have everyone stepping on each other’s toes. I mean what the hell really differentiates Damian and Jason nowadays? Both are dark and edgy boys who are tempted to use lethal force but don’t because they want Daddy to be proud of them. Tim is completely overshadowed by everyone else because “bland self-insert” doesn’t hold up compared to how cool Dick, Jason, and Damian are, so they made him the gay one to give him something. They turned Babs into Steph for the Burnside era. You make Jace part of that, he isn’t going to stand on his own two feet because every character personality type imaginable is already present in the Batfamily. All that’s left is to be the guy who appropriates their brand but does his own thing without their approval.
2. Nightwing’s inability to stand on his own is because his runs keep getting derailed by having to tie into Bruce’s bullshit. You make Jace part of Bruce’s family, now he’s subordinate to Bruce in the pecking order, he’s going to be constantly reacting to whatever the storyline in Bruce’s book is.
3. Jace being Batman is always going to be weird if he’s part of the Family because why does he have the mantle when Bruce is still around? Why doesn’t Dick, or Tim, or Damian take it? Why not Luke or Duke? You’d have to make one hell of a contrivance to justify why the newcomer gets to be Batman over any of the guys who have “earned” it. Jace only works if he’s Batman because he’s the one who decided he wanted that role and just took it, Bruce and the rest of the Batfamily be damned.