So play the merit card: ask for an evaluation of prediction-of-merit vs. demonstrated-merit (by whatever mechanism they favor--product of citations and impact factor, or whatever).

If the competitions are actually rigged, there won't be a great deal of correlation between predicted-merit and demonstrated-merit even by their own standards whatever those may be. You can run a multiple factor analysis including whatever seems relevant--funding in home country for instance--to try to isolate where the current method is failing to adequately provide funds for meritorious research.

If the competitions are not rigged (e.g. because doing science at that level really is that hard and you really do need a well-funded lab to even get a decent start at the problem), you can still end up in an unfortunate situation of citation circles between academic royalty, and that is much harder to detect--for instance, you might need to assess the replicability of the research to detect such things.

If the competitions are not rigged, and the research is reproducible--the royalty is royal because they really are good at what they do--then there still may be some degree of control over the direction of research overall. That won't stop most people who want to from playing the science game and thereby increasing our store of reliable knowledge. It may, however, stop people from playing the game that would be most useful to humanity or would be most fun for the researcher. That is a shame, but less of a shame than being rigged from the outset.