That's one possibility. But there's also the possibility that encouraging presenteeism (which is what incentivizing hoarding sick days is) results in a net loss

That's one possibility. But there's also the possibility that encouraging presenteeism (which is what incentivizing hoarding sick days is) results in a net loss of productivity as sick employees both half-ass their work and also get their coworkers sick. Which a profit-driven entity should care about.