I have been thinking recently how to reform the science system here in germany, which is somewhat similar to the system in the US. What I think is impossible is to completely eliminate the grant chasing for the early career scientist. It's just that there's more supply than demand in a lot of sciences and not everyone can make it, if we try to give everyone a grant we end up with grants that are not really paying for anything.
What I think would be an improvement would be a different system where there's a clear path from grant-based funding to a continuous stream of funding, with different funding levels, where one gets periodically reviewed and demoted/continued/raised, so your funding does not completely dry up after a few year (I imagined it like the sports leagues, where you play in different levels and depending on your performance you get relegated from the league) and you can really plan long-term. So one can continue the competitiveness and the role of funding bodies/institutions where the scientist work at while giving them the ability to plan long-term and maybe pursue more risky ideas.
There will always be the ones that fall through the cracks. We somehow need to figure out who to give the money to and we will end up with someone who deserved but did not get the money. I don't know who reviews the grant in the US, but here at least with some funding bodies the scientist manage it themselves (dfg) and I don't think one can easily improve on it.