The importance of this relationship is not only the different abilities and skills they bring for the greater good or their different personalities which creates for entertaining dynamics. They are a team, yes, but they are also close friends and family. They have built up a lot of trust over the decades, and sometimes have had disagreement, but ultimately they have a lot of affection for one another. Clark is the glue that keeps this Trinity together, I feel.
I love Clark and Diana as a couple, and their innate optimism and compassion I think helps Bruce and tempers that loneliness and darkness that surrounds him. That they do this unconditionally is what makes their open heartedness so significant. For me Bruce sees them as the brother and sister he never had.
The greatest testament of their trust, love and respect is seen when they ask him to be Godfather to their child in Kingdom Come. The timing of it is perfect too because it is all earned via the narrative of hope overcoming tragedy/ light triumphing after darkness. Bruce, of course, says yes. I mean, the idea of training and influencing a Kryptonian/Amazon kid, I can just see a seasoned and older Batman would love that!
It’s also why I think Kingdom Come is such a great story and seen as a perfect finale to the DCU. It ends on a high note and a whole epilogue celebrating the Trinity.