I’m pretty sure one of the reasons Tim and Bruce got along so well during a time in which Bruce had such turbulent relationships with others was due in part to the incredibly low standards Tim had for parenthood.
Dick, among others, found Bruce too demanding and controlling, and understandably so, because Bruce was so very paranoid. But Tim had been accustomed to an authority figure that constantly ignored him, and having Bruce so concerned for him often touched him more than it bothered him.
Bruce was also conflicted in his own mind. He referred to Jason as a “good soldier” almost as if he were trying to distance himself from the fact that Jay was also his son, because he’d never seemed to reconcile the fact that he was in a close relationship with young folks he was constantly sending into danger. So it was easy to find ways to push others away.
Except that Tim kept his distance automatically. Tim really did act like a soldier or employee much of the time, reinforcing his working relationship with Bruce far more than their personal one. So for once, it was Bruce yearning to be closer to someone. And Tim was okay with the status quo, because it was so far beyond anything he’d had before in his life.
Now I’m imagining how completely CONFUSING this would be for a time-traveling Damian. If he got jettisoned back in time to when Tim first became Robin, he would expect their rivalry to intensify all the more because after all, Timothy had just barely earned his stripes. But instead… Tim and his father would hardly act like family at all. And it would feel wrong. Because Timothy is the favorite, or that is how Damian has always perceived him. And Dick might be less welcoming, because he’s actually terribly protective of Tim at this point and… hmmm. it would just be fun.