The problem is purely one of incentives. If you design a pathological system and make highly intelligent people use it then don’t be surprised with the terrible results.
The solution to science is actually very simple - move from a peer review ranked grant allocation system (which is totally gamed by those at the top) to a basic screen and lottery system. The idea is to do a basic screen on grant applications to make sure they are scientifically viable and not majorly flawed (at least 75% of grants should pass this test) and then put them all into a pool and draw winners from this pool until you have allocated all the money you have.
Lets stop using a system that can’t actually do the job (peer review can't separate the top 10% from the top 20%), and which is open to corruption and old boy networks, and move to one that is at least fair and better than all the alternatives.
Or you could take the anarcho-syndicalist approach and split the money evenly to the entire pool, with a lower bound on grant size which makes the money inconsequential and if the lower limit is reached require all grantees to contribute a portion of their time to growing the money pool.
Two problem with this idea. If you don’t have some sort of barrier to entry then anyone can apply for a grant. This funding is made available on the basis that it will be used for science. I know this sounds elitist (it is), but science is really hard and it takes many years of learning to reach the forefront of knowledge where you can actually make a contribution. You only want to give funding to those that can actually use the money to do science. It would be a good idea to have another pool open to everyone to see if this barrier is really required - it might actually not be.
The second problem is if you split the money too much then you won’t actually be able to do any research. To see an experiment through to completion requires a not insignificant amount of money (in most cases). If you start to hand out amounts of only a few thousand dollars at a time then nobody would be able to get any done.
Under an anarcho-syndicalist system you don't need to worry what your neighbor does with their share. You have your share. If you want to work towards a common goal you need to convince them to work with you voluntarily.
I addressed the second point in my original post but maybe that was unclear: if there are so many applicants that individual grants become too small to serve their purpose, you stop accepting applicants. But then you require the applicant pool to spend some portion of their time growing the grant pool until the waiting list is empty. Flipping burgers if need be. Although we're talking about PhDs so I am sure there are better ways to use that labor pool.
Stopping the acceptance of potential grantees is just putting an inefficient barrier to entry of new people. The end result of limiting people rather than a base quality is that it would favour the old over the young which I don’t think is a good outcome.
You will have to argue it's less efficient than the current system. You can't just state that it is so.
As for favoring the old, all you have to do is require people to regularly re-apply. There's no reason you need to hop the line after the end of your term.
And you seem to be assuming that the waitlist will be prohibitively long, but the longer the waitlist the more labor you have for growing the grant pool, so it naturally self-regulates.
The solution to science is actually very simple - move from a peer review ranked grant allocation system (which is totally gamed by those at the top) to a basic screen and lottery system. The idea is to do a basic screen on grant applications to make sure they are scientifically viable and not majorly flawed (at least 75% of grants should pass this test) and then put them all into a pool and draw winners from this pool until you have allocated all the money you have.
Lets stop using a system that can’t actually do the job (peer review can't separate the top 10% from the top 20%), and which is open to corruption and old boy networks, and move to one that is at least fair and better than all the alternatives.