Yes, but psychologically speaking, the difference between "somewhat randomly" and "totally randomly" is huge. With the latter, you lose the incentives, because it doesn't matter what you do. In capitalism, there is a lot of randomness on who gets rich, much more than in grant reviewing, and while capitalism can be criticised from many angles, even the staunchest anti-capitalists wouldn't deny that it's great at incentivising people to try to make money...
The variant you mention would be better than pure randomness, but at least for me, it wouldn't work either. First of all, in order to become "excellent" at research you typically have to start at "good enough", so the "excellent" category would also be hugely conditioned by the randomness - how do you build up an excellent CV if you repeatedly lose the grant lottery? Secondly, although incentives wouldn't be totally lost, for me it still wouldn't work psychologically. I can come to terms with the fact that there is a large random factor in grant reviewing, it's not something I like but that's just life and very difficult to avoid, but I wouldn't be able to accept seeing the researcher next door scoring a grant while I'm left without it due to a pure lottery, to be honest. I think I would go to industry.
PS: regarding what you mention about marketing, something I would do would be to evaluate people (CVs) rather than project proposals. Proposals are indeed very, very biased by marketing and by how boldly researchers can make grandiose claims (which is likely to be correlated negatively with research integrity). And in CS they often don't even make sense... for example I work in NLP, large language models like BERT came in 2017-2018 and revolutionised the whole field, if I had followed the text of my ongoing grants to the letter I would have been doing obsolete research. (I can see how in other fields like physics, etc., this may not apply).
The variant you mention would be better than pure randomness, but at least for me, it wouldn't work either. First of all, in order to become "excellent" at research you typically have to start at "good enough", so the "excellent" category would also be hugely conditioned by the randomness - how do you build up an excellent CV if you repeatedly lose the grant lottery? Secondly, although incentives wouldn't be totally lost, for me it still wouldn't work psychologically. I can come to terms with the fact that there is a large random factor in grant reviewing, it's not something I like but that's just life and very difficult to avoid, but I wouldn't be able to accept seeing the researcher next door scoring a grant while I'm left without it due to a pure lottery, to be honest. I think I would go to industry.
PS: regarding what you mention about marketing, something I would do would be to evaluate people (CVs) rather than project proposals. Proposals are indeed very, very biased by marketing and by how boldly researchers can make grandiose claims (which is likely to be correlated negatively with research integrity). And in CS they often don't even make sense... for example I work in NLP, large language models like BERT came in 2017-2018 and revolutionised the whole field, if I had followed the text of my ongoing grants to the letter I would have been doing obsolete research. (I can see how in other fields like physics, etc., this may not apply).