As strange as it sounds, a detective that runs and does things quickly could actually work if Devil May Cry’s Dante Sparda’s any indication. He’s said to be a detective and mercenary and actually has super speed himself. It’s actually not much of a stretch for Barry Allen, who as a speedster, to have more of an affinity for escapology and tracking. If you run real fast, that’s useful for easily escaping bad situations.
There’s even a folk tale where a girl averts her ordeal by just running away from the wolf. That’s not to say Barry’s dumb but that involves him actually outwitting or avoiding his opponents without being so overpowered in the most realistic way. Sometimes if something’s going to charge at or kill you, move away. That could’ve been done before.
It wouldn’t matter at what speed Barry runs, what matters is if he survives long enough to even averting misfortune. The biggest problem is that even if there are people who do things real quickly and likely so did he, Barry’s now more jock than nerd. Even if it’s not always exactly the case especially when those at team sports get bullied themselves.
But that it gives an idea of what’ll happen when Spider-Man’s Flash Thompson becomes super-powered, without succumbing to Venom or something. Even odder still, Barry Allen’s what Flash Thompson would be like if he were also Peter Parker. (Logically Green Goblin’s both Joker and Lex Luthor.)
Usain Bolt’s the fastest human alive and is now currently playing football. Despite having different ethnicities, one gets the impression that’s what Barry Allen’s like if he were real though it could be me being interested in sports and having somebody who runs every weekend. (I do hazily remember playing football myself.)
Realistically, even if Barry never became a detective he’d be a combination of both Harry Houdini (escape artist) and Usain Bolt.