I've actually worked at a place that did something like this, although I suspect it wasn't for positive reasons. It was a call center, and they had status tiers for wages - e.g. if you were an "A player" you would get $.50/hr more, or if you were a "star player" you would get $1/hr more (or whatever the amounts were). These statuses were tied to various metrics that the business cared about - average call time, quality scores from customer surveys, repeat calls, and so on. So ostensibly, if you got the current metric down to whatever the goal was, you would get a raise for a month or whatever.
The problem was that the business changed these metrics on the phone reps all the time, so it was common for some poor bastard to really strive to get his call times down, only to be told "oh sorry we're focusing on quality scores this month" when reviewing his work with the boss. My impression was that the company was doing this to avoid having to actually pay people more, not to keep people from gaming metrics - but I think the results would be pretty similar regardless of motive.
What happened wasn't that people focused on trying to be great generalists. Instead they got demoralized by the games the company was playing, and they would either quit trying to improve at all or they would exclusively focus on one metric (so that they could get the big raise when that metric was being rewarded next).
Based on that experience, I'm somewhat doubtful that what you propose would work. But it might - unfortunately the workers at that call center were very often real fuckups all around, so the idea might work at a business which has better quality employees.
The problem was that the business changed these metrics on the phone reps all the time, so it was common for some poor bastard to really strive to get his call times down, only to be told "oh sorry we're focusing on quality scores this month" when reviewing his work with the boss. My impression was that the company was doing this to avoid having to actually pay people more, not to keep people from gaming metrics - but I think the results would be pretty similar regardless of motive.
What happened wasn't that people focused on trying to be great generalists. Instead they got demoralized by the games the company was playing, and they would either quit trying to improve at all or they would exclusively focus on one metric (so that they could get the big raise when that metric was being rewarded next).
Based on that experience, I'm somewhat doubtful that what you propose would work. But it might - unfortunately the workers at that call center were very often real fuckups all around, so the idea might work at a business which has better quality employees.