If the easy things fail (usually the financial or flexibility kind) there are other options. Find them the same position in a different team with different dynamics (a great individual can sink if everyone else on the team is much better, or much worse), find them a different position where they can shine (you can start as a mediocre midfielder and end up a successful goalkeeper), or even have them find a different job entirely.
After a worker has achieved a base level of income that makes their life comfortable, any extra treats they receive will decrease their interest in the core function of their work, moving their focus to the extrinsic motivator instead.
I've also heard interpretations of this effect that explain it as: being rewarded can demean the value of work, because it may feel as though the work itself is a chore that nobody would do unless they got rewarded.
In general, I believe that extrinsic motivators lead employees to follow their instincts less and focus on anything that will net them a reward. This means that even if someone has a great idea for improving some aspect of the work a company is doing, it might not get done. They are instead being rewarded for whatever arbitrary KPI that management has decided is important.
In fields where there is a single clear KPI, all processes are mature, management has a clear view of the entire value chain, and workers are focused on a single task that is highly tied to the KPI --- e.g. yields in manufacturing tied to a production line worker --- sure, rewarding high KPI is not a terrible idea (or at least as terrible as it would be otherwise). But whenever a workers focus can be co-opted by bonuses I believe bonuses tied to KPIs are a bad idea.
RE: your second point, I absolutely agree. How well a person "fits" in a team has a high impact on a person's motivation.
1. "The Effects of Contingent and Noncontingent Rewards and Controls on Intrinsic Motivation", 1972, Edward L.Deci, [Available online] http://selfdeterminationtheory.org/SDT/documents/1972_Deci_O...
2. Punished by Rewards, Alfie Kohn, 1999, https://www.alfiekohn.org/punished-rewards/
3. "Intrinsic and Extrinsic Motivation ", Roland Bénabou & Jean Tirole, 2003, https://academic.oup.com/restud/article-abstract/70/3/489/15...
4. Intrinsic and Extrinsic Motivation - The Search for Optimal Motivation and Performance, Carol Sansone & Judith Harackiewicz, 2000 https://www.amazon.com/Intrinsic-Extrinsic-Motivation-Perfor...
5. "Intrinsic and Extrinsic Motivation", Lisa Legault, 2016, [Available online] http://www.lcwu.edu.pk/ocd/cfiles/Professional%20Studies/FC/...
6. "Do intrinsic and extrinsic motivation relate differently to employee outcomes?", Kuvaas et al., 2017, [Available online] https://www.researchgate.net/profile/Bard_Kuvaas/publication...
EDIT: added more recent sources
Oh, this is a slightly different topic. Of course if your belly is growling money will motivate you a lot, and that motivation tends to go down the more you go past your comfort baseline.
But think of pay disparity for example. Maybe your belly is full but your slacker colleague is making more money than you. That has a good chance of demotivating you, making you ask "why should I try harder?". Reducing this disparity and (perceived) inequity, eliminating the demotivating factor, goes a long way and has a far longer lasting effect than just the same extra money would bring otherwise.
And pay disparity can be a problem, especially if salary data is hidden. I think most of the time the problem is a lack of openness about salaries and why they are as they are.
As if my additional efforts are not going to move the needle much and there is nothing individually for me to win, why not just enjoy the ride?