Well, it’s not precisely true that a third baseman must be a slugger; no one had a problem with Wade Boggs at third baseman and he wasn’t a slugger. Of course, he won five or six batting titles, so that helps.
They’re not, exactly.
Obviously all teams would PREFER to have elite hitters at every position. If your shortstop is Alex Rodriguez or your catcher is Joe Mauer that is a wonderful thing. However, that’s a rare gift.
What it comes down to is not that a team wants to trade off defense for offense, but that they often have no choice. There simply are not as many MLB-quality shortstops around as there are MLB-quality left fielders, because it’s just a way harder and way more important position to play (and also, of course, because lefthanded players can’t play shortstop.)
A Major League Team has in its employ over a hundred professional baseball players and can acquire any number of players pretty easily and cheaply. It is just really, really unlikely that a team will ever find itself in a position where it cannot find a player who can hit and play left field or first base passably well. There’s always a left fielder you can get if your current one can’t hit. On the other hand, the number of players who can play MLB quality shortstop is comparatively very limited, and there is an excellent chance you will be left with no good shortstops who can also hit well.
In addition to deficiencies of skill, different positions vary in importance. Third base is an interesting example in that third base is a VERY hard position to play; ir requires an excellent arm and a fast reaction time and is brutally unforgiving; that’s why third baseman have lower fielding percentages than any other position. The reason third basemen are not considered as defensively valuable as shortstops is simply that they are not asked to make as many plays. A typical third baseman will handle 350-400 chances in a full season; only a handful of third basemen have made more than 400 assists in a season. A shortstop can get 700 chances or more in a season, and 400 assists would be a terrible year. If you had two guys who could play both SS and 3B, you’d want the better fielder at SS just because there are more plays to make there.
First base is the opposite extreme; first baseman make more plays than anyone, save the catcher, but they’re almost all just catching throws. First basemen rarely need to make throws at all and don’t cover as much ground as other infielders. (Steve Garvey could barely throw at all, and he was a pretty good first baseman.) Of course not any schmoe can play first base at the MLB level, but, realistically, the difference between a poor MLB first baseman, like Cecil Fielder, and someone who’s clearly really good at it, like Todd Helton, isn’t all that much. A bad first baseman (again, by MLB standards) is irritating but you can live with it if the guy mashes. A bad shortstop will just kill you; if your shortstop sucks with the glove but can hit, it is virtually certain that you are in a position to move him to a less demanding defensive position and find a shortstop whose glove doesn’t cost you two runs a week.
It is of course quite possible a truly elite defensive player at a middle-importance defensive position like right field or third base could be very useful to you even with a mediocre bat; Charlie Hayes, Glenn Wilson, Scott Brosius and others were all players of limited bat reliability but really outstanding glove men at those positions. It’s unusual, though.