It follows the distribution of skill points in D&D 3rd edition.
The rogue has the most trained skills in D&D 4th edition because it also had the most skill points in D&D 3rd edition (8 per level; 3e had more individual skills than 4e). This in turn goes back to the original thief class as it appeared in the supplement Greyhawk (1976), which was originally the only class in D&D to have a fixed percentage chance to succeed at tasks like Open Locks or Move Silently.
Rangers and bards had the next-highest skill points per level in 3.5 (6 per level). Artificers had 4 per level, but they tended to have bonus skill points from high Intelligence because that class used Intelligence, making the artificer a high-skill class in practice.
Next in 4e is the four-skill class, which seems to be a default base number of trained skills in that edition. The majority of 4e classes have four skills unless there is some reason otherwise.
The fighter had the fewest skill points in 3e (2 per level), and this status seems to have been carried over. The barbarian had more skill points in 3e (4 per level), but appears to have been relegated to the fighter-type low-skill category in 4e (perhaps they only had 4 skills in 3e on the assumption that they would take low Intelligence and lose one or two skill points, whereas the 3e fighter could more readily take the Expertise feat chain requiring 13 Intelligence; this meant in practice 3e fighters often got 3 skills from the +1 Intelligence modifier, and barbarians sometimes fewer from a dump-stat Intelligence score of 8, again 3 skills). We might also speculate that both fighter and barbarian get 3 skills because it was the average of the 3e barbarian and fighter number of skills; a complaint among 3e players was that fighters got few skills and couldn't do much interesting outside of combat. 4e also converted a lot of the fighter's strength-based skills into a single skill, Athletics, which may explain why it doesn't get 4 skills any more in 4e.
The battlemind didn't strictly exist in 3e for comparison, but its closest equivalent is the psychic warrior, which is essentially a psionic fighter, and also shares the 3e fighter's low skill count.
In short, the closest predictor for the number of trained skills for each class in 4e is not the usefulness of the skills they have available, but rather the number of skill points they got in D&D 3rd edition.