Not sure to be honest.

I think the main problem of the current setup is that the science teams are not balanced enough.

The radar sounding science team is mostly geophysicists because the interpretations are geophysical in nature, but there are not enough people who are experts in radar sounding, radar system and radio frequency wave propagation in general. The reason for that is, that this is not considered science and is looked down upon as mere "engineering".

Privatized exploration would initially solve some of these problems for sure, but once a group of people and its structure has manifested I believe they would eventually suffer from the same problem.

Anyway, this is a pretty complex topic which covers many aspects such as research funding, incentives in academia, vain egos, etc.

The public sector doesn't have a monopoly on internal politics. Posturing between departments to be included in the next big initiative happens in lots of companies.

The point of competition is that if 10 deeply flawed organizations take a crack at a problem, they won't all produce garbage.

That's not guaranteed. Really it's a question of incentive structure more than public vs private.

For example there are cases I can point to of poor competition and high costs in NASA picking private companies to do big cost-plus development contracts, and cases where they did fixed-price contract bidding among a larger pool of competitors and got much better results.

While that might be true the costs of going up there are so high that there won't be 10 companies who get a crack at it.

Besides, the radar isn't the only instrument on the rover. There aren't many companies/groups in the world who have the know-how and financial means to do what NASA does here.

Or! They all produce garbage as they chip away at costs, and make bank telling people what they want to hear. The incentives are all wrong.