First, the premise is a bit wrong, because applying for grants does generally involve a good deal of valuable work: careful review of what is known, careful consideration of what can be done, etc.. But that there is too much of that is probably true.
For alternatives, one can look to a variety of historical and current examples of low-effort funding within a particular institution.
Perhaps the classic example is Bell Labs. With a gargantuan research budget paid for out of Ma Bell's monopolistic phone rates, Bell Labs could assign resources to individual investigators with a minimum of fuss. The system there was relatively hierarchical, with people in higher tiers responsible for the scientific quality, and to a lesser extent the budgets, of those in lower tiers.
Another classic and current example is the U.K. Medical Research Council's Labs for Molecular Biology (MRC/LMB). Researchers at the MRC/LMB have to spend only a minimum of time justifying their budgets, and a maximum of time producing high-quality science that justifies their continued position at the MRC/LMB.
A new example is the Howard Hughes Medical Institute's Janelia Research Campus. Lab heads at HHMI/Janelia have to do little more than specify the budget that they wish and justify that any large expenditures are likely to yield equally large rewards. There are reviews every few years to ensure that researchers continue to do high-quality science.
These examples are not at all exclusive. Researchers in many industry positions need spend relatively little effort on grants. Likewise for various other research institutes (though many allow researchers to spend their time trying to get additional grants, if they wish).
So, in brief, the alternate model is: pick people, not projects, and trust that the best people will, on average, do the best work. Have some sort of periodic review process to ensure that the best work is, in fact, being done.
Note that this is not necessarily any more kind to people who are having trouble with their current line of research. In fact, it can be even harder--there is little mechanism other than having a high-productivity line of research that will keep one from being kicked out to make room for someone judged "better". But this possible disadvantage may be worth the advantage in letting so many people with so much talent spend more of their time directly using it.