Isn't that what Dante does already? Yeah, he would be more of a bounty hunter but it's a bleak difference. You call Dante up, he sees if you're issues fit his requirements and he takes care of your otherworldly woes. Yeah, we don't see it in the games but honestly, who'd want a run of the mill everyday case for a whole game?
Only
kinda. Capcom's whole shtick now is making Dante a sloppy, careless "investigator" that shrugs at demonic cases that are dropped onto his lap from somewhat reliable sources (see DMC4). In terms of character, there's no reason Lady had to bargain with him to go to a place where they were
collecting Devil Arms and the cult's soldiers involved themselves in other demon-hunting related jobs. He was supposed to be the guy that jumped on cases as long as anything remotely demonic was involved [regardless of the money], but DMC4 was him shrugging at everything Lady said, making a spectacle of murdering a cult leader and terrorizing innocent worshipers, but then a minute later he decided he was finished being proactive and said "Let's see what happens"-- he allowed Nero, the terribly inexperienced punk that he is, to go off into a situation he wasn't ready for, and passively let stuff escalate to the point where Sanctus awakened the Savior and opened a Hell Gate leading to hundreds of civilians dead, when that entire conflict could've been nipped in the bud in a half hour of Dante
doing something other than standing around being cryptic. Considering how much more powerful Dante is portrayed compared to anything in the game, DMC4
was his "everyday" job, and he just happens to
suck really friggin' bad at it. That's how he is now. He's not serious anymore.