You're right, he'd be their number 4 instead.
You're right, a 4.23 career ERA isn't impressive. It's solid, which is exactly what Bronson is. Just because he doesn't have a 10 K/9 ratio you think he's BAD? You haven't provided a single shred of evidence to suggest he's bad other than the fact that you just happen to think so. Considering his home ball park is literally THE most hitter-friendly ballpark in baseball (besides like Coors damn Field, but they're like 50,000 feet in the air lol), I'd say he does pretty fucking well.
I linked you to his stat page while referencing his stats, but if you'd like it in more detail, I'll be happy to oblige. He is, and always has been, one of the most homer friendly pitchers in the league. This isn't just a function of his home ball park, either. Admittedly, the GABP has one of the highest HR only park factors (though as a note, it isn't nearly as exaggerated as you stated, it consistently ranks top 10, though), he still has a career 1.18 HR/9 on the road.
Earlier in his career in Cincinnati, he wasn't just a bad starter who ate innings. He provided marginal value in those innings because he could still strike out some batters. I appreciate that you think I need his K/9 to be 10, because obviously, greatly exaggerating someone else's stance is a way to prove them wrong. He's at a point now where he's striking out far less than the league average, at a time when the strikeout ratio is only increasing. This year, the National League strikeout average was 7.69. His ONE YEAR spike was 5.75 (whereas his previous three years had an average closer to 5). That's a difference of two.. that's more than substantial.
But what if strikeouts don't matter (even though they obviously do)? Arroyo's pitching style is even more detrimental than most in that scenario. He's a 60% FB pitcher, with at minimum 10% HR/FB. This means, that Arroyo, in comparison to most pitchers, allows more balls in play (because he doesn't strike out many batters). Which means he allows more flyballs than most pitchers. And we get the homeruns.
You can be a pitcher like this if you "have the stuff to get away with that". There's a reason people say that: striking out batters removes ball in play, which always increases the likelihood of a positive outcome for a pitcher.
There was a time when you could argue that Bronson Arroyo was solid, especially relative to the league average (say, 2005-2008). Unfortunately, Arroyo's performance has generally been getting worse, at a time when league average (especially the National League), has been getting even better. This means that his value relative to other players has been getting even lower. When you take into account the Cincinnati defense (who, from 2009-2012 are ranked #1 in Defensive Runs Saved, and #2 in Ultimate Zone Rating), you see that Arroyo is a a bad pitcher who's ONLY value is innings, who's been saved the disgusting stat-line on balls in play thanks to a defense with some of the best range in all of baseball (as evidenced by his 4.79 FIP, and 4.5 WAR, second worst (to Jeremy Guthrie) and worst among pitchers with 700+ IP over 2009-2012)