What do you think would be the effect of giving out awards for the best open source code on GitHub or whatever?

My theory is that awards would actually make people to stop working on less significant repositories (that clearly cannot win the awards) and focus on the major repositories, the most starred and forked ones so as to get a share of the prizes. Maybe there would be times when commits(which are way better than the current code) are not merged onto the main branch coz doing so would introduce another coder in sharing the prize. The clustering of everyone's efforts on the major repositories would leave the less significant but useful repositories neglected. Can't say the number of times I have copied code from these repositories. I think awards would be disruptive to the open-source Ecosystem. Am high and am out ppl. Go savage the comments. Wait do such awards exists...haha.

Not sure how you'd choose the "best" open source code, but...

Back in the day Sourceforge used to do something similar - they had a highlighted open source "project of the month" or similar. Not sure there were monetary prizes involved, but certainly lots of publicity and I think vouchers from sponsors (don't quote me on that.)

It was ridiculous. I only ever saw projects featured that everyone knew about already, and certainly didn't need lots of extra publicity.

Now they've changed it to keep the name and feature smaller projects - but aside from being featured a bit further down the frontpage on a site no-one uses anymore, there's nothing in it.

Read more about intrinsic and extrinsic rewards.
If you are talking about "abstract loyalty rewards" like points/stars or awards like badges then your question falls under intrinsic rewards, which already has been implemented by GitHub, also used by Stackoverflow, Quora and the likes... This reward pattern has more pros than the latter which involves physical or cost inclusive awards (extrinsic reward). Most repo contributors would be more focus on the award rather than for the love for its creation and maintenance which in turn slowly kills "the motivation to create" and increases "the motive of earning vanities", and when the love for creation goes down, maintenance goes down followed by dedicated contributors.
GitHub "stars & badges" already cover up for rewards with stars and awards with badges using intrinsic pattern. If they tend to go with extrinsic reward involving monetary cost or material award (which I hope is not what you meant) that will affect their contributor's loyalty.