Not to demean Abreu's by all accounts very workmanlike approach to hitting, but hearing him say he doesn't try for home runs is at best a semantic argument. He emphasizes driving balls in the air and getting his arms extended, and with his power, there's not much mystery on what's going to happen when he does that. He's not shortening up, choking up on the bat or trying to slap the ball onto the ground, because that would be dumb and a waste of his time and talent.
But at the same time, he's not the not only plus-powered first basemen with Derby anxiety. He's not the only one who even spoke the media Tuesday on the topic. Diamondbacks first baseman Paul Goldscmidt also said he would decline if asked to participate--Abreu sounded more like he would like to decline, but wasn't entirely confident that he would have the leverage to do so.
Despite the Home Run Derby being a batting practice competition, Goldschmidt asserted that the event would take him out of what he generally looks to accomplish in batting practice.
Despite their obvious amounts of personal experience, players are not magically immune from buying into anecdotal speculation with no statistical basis. Chris Sale and John Danks are both more or less luddites about advanced statistics and win-loss records, for example, and the wisdom of "pitch to contact" is it's own muddled rabbit hole for discussion. Point being, players having concerns about something is not a case-in-point that it's a significant issue.
But in the age of all-consuming analysis and review, where players are encouraged and evaluated for their ability to probe for advantages and squeeze every ounce of value from their abilities, it's not surprising they would come to view the departure from preparing for in-game situations an unnecessary distraction.
Despite it's silliness, the Home Run Derby strikes me as a necessary antidote to some of MLB's optical troubles, where they battle the perception that the sport lacks high-level athletes. The Derby offers an opportunity for players to display their extreme physical gifts and entertain, but since players are evaluated in a way that encourages to approach their jobs like a sales gig, any time that's not dedicated toward boosting their in-game production is wasted time.
MLB could just force healthy players to compete, but have a hard enough time doing that for the actual All-Star Game, and have enough of a "Pretend like you're having a good time" vibe going as is. If these guys cannot be convinced this is worth the risk and time, the onus falls on MLB to convince them otherwise and demonstrate how much they are willing to do.