I was more concerned that Superman was a reporter who didn't know who Bruce Wayne was.
"George, you can type this beep but you can't say it."

Benny's real good at finding missing candy bars. And nannies who'll take him for everything. He's sort of a fat Columbo.
You're welcome.

If Batman is such a great detective
This incarnation isn't that, though. That's just something we have to accept. Maybe he was more of that in the past (we dont know), but now he's primarily an aging brawler who relies heavily on his computer and his butler for the investigating part.

Because this was a more human version of Bruce who had succumbed to his emotions which blinded him. Personally, I prefer a more human Batman to Batgod. I can relate and appreciate the former more. There used to be many interesting storyline in decades past when Bruce/Batman was fallible.

Snyder does not like the idea of Batman being intelligent it would seem in his universe Lois is the intelligent one who does the investigating.
To make a great film you need three things - the script, the script and the script -Alfred Hitchcock

Because Zack Snyder!