Clint has OCD. They work with it. After all, this is the Avengers; everyone's got quirks

"Tony Stark sometimes doesn't make the best choices with his health. Tony is usually bad at communicating. Steve usually doesn't end up in medical, but there are always exceptions. "Phil Coulson is the one who has to write up this nonsense, and he can't keep the Avengers out of medical."

Phil looked at Clint, lowering his weapon, devastation clear on his face for a fraction of a second. Devastation for what Clint had done, or devastation for what he’d suffered Clint wasn’t sure. He squared his shoulders regardless. “People like to say that blood smells like iron, but it doesn’t. Blood smells like blood, and sometimes there’s no way around it and no room to regret it.”