my opinion on the royals problem hitters based on eye tests (keep in mind, i know nothing about baseball). with recommendations on roster management.
moose - he's a shitty hitter. he just doesn't have good hand-eye coordination or whatever it is that lets hitters hit baseballs consistently and he's never going to hit for a good average. when he manages to make contact, he has good power. he's ok at distinguishing balls from strikes. it's not an approach thing, it's just his natural ability.
keep him as long as he's cheap. whenever he has had enough time in the league that his salary is higher than other equivalent players, dump him. or if the royals develop a better homegrown option (lol). any replacement that isn't significantly better will need an animal nicname.
hosmer - he's well above average at hand-eye coord, he's just Fake Sugar Dick (WARNING, NOT THE REAL SUGAR DICK!) or blind or has some other problem that makes him swing at horrendous pitches. if he could stop doing that, he'd hit for a v. good average with decent power.
give him a couple of years to stop swinging at stupid pitches (and punish him for not learning during that time). if he hasn't gotten smarter by then, dump him.
butler - he's going downhill. he's not that old, but some people decline precipitously. he's lost both power and the ability to make contact. it sucks that formerly one of your best players got the baseball equivalent of cancer at 40, but it happens. dump him either now or at the end of the season and use the money elsewhere. you aren't going to get a great replacement for the same salary unless you get lucky, but you can probably get a fairly equivalent replacement much cheaper and use the money to improve other positions.
for the rest of the year, i'd have no problem just rotating the dh spot around the current roster plus whoever they can pick up free as long as it doesn't mean keeping maxwell on the team. but they could keep butler too, just as long as they don't extend him for next year and beyond.
