You are right that clubs don't produce "kinds" of players in the sense of "goalscorers" or "great tacklers". However almost every club academy website I looked at claimed to be looking for "particular types of players for their academies". For instance, Tottenham says "
Tottenham tend to look for a particular type of player for their youth Academy. Players who are highly skilled but many of them are lightly built and their stature and physique may be a hindrance when it comes to that final step up in professional football." (
LINK)
And from the BBC: "
Manchester City's chief football operations officer Brian Marwood has said the club's new academy is an attempt to create 'a different type of player'." (
LINK)
This doesn't mean they're going to create superstars, or increase player potential ability in our analogy here. It just means that different academies have different staffs with their different skill proficiencies, etc. that ultimately add up to slight, but fairly consistent, differences in skill development (though these differences can become more pronounced with very smart teams, like Barca. Maybe they just have the right set of staff to produce players with the skills that will fit into the clubs strategy and tactics, which is what makes them so good. You just start with the base (random) stats, and adjust a few of them up and down (based on this choice) so there's no net change in stat figures. Furthermore, it doesn't guarantee anything:
Say you like to use the Man marking tactic and so you set your academy setting there. The random-stat generator pumps out a defensive player who is naturally suited to Zone marking (by chance) with low stats in key stats for Zone. By subtracting 1 or 2 points from Zone stats and adding them to the Man marking stats yes, the player would become better suited to man marking (and worse at zone marking), but they would still stink at Man marking. So a 1 point change in those key stats would only increase the likelihood that you would get a player that was better at your preferred tactic by 5%. That makes the
increased probability that your academy will produce a player that is best suited to all 3 of your primary tactics close to zero (5% cubed = 0.000125).
That would be level 3 or 4; level one would only get 1 out of 3 or 4 stats weighted this way. Level 6 might double this, offering a 10% odds increase (1/1000 for all 3) which is a significant, yet far from overwhelming incentive for upgrading this expensive facility.
Maybe instead of decreasing the cost of facility upgrades, there should just be more benefits that come from them...
edit: checked math