That's the point, though. Baseball players earn a tonne on average, but very little when they first enter the league; generally, a pre-arbitration player makes $500,000, no matter how good they are. Mike Trout very nearly won the MVP as a rookie, and he's making (IIRC) $520,000 this year.
Basically, there are three tiers: pre-arb, which lasts for the first three seasons of a player's career (unless they hit Super Two status, which is based on service time and results in salary arbitration for their third season), three years of arbitration, and then free agency. So there are six years there where the player is tied to their original team, and the salary they earned is significantly below what they would make on the open market, though arbitration figures are starting to escalate to sums closer to free agent value. Those are the cost-controlled years that I mentioned, and they're a huge deal; a league-average player might cost you $7-10m a year in free agency, so if you have two kids making $1m combined filling spots and producing league-average results, you then have a huge pile of surplus value that allows money to be allocated elsewhere.
Ah yes. Didn't read your post properly. But these young players know full well if they become a top player they will earn a massive contract through free agency.