I'd like to see an option to exclude specific external indexes from my search.

The benefits I see are these:

Improved Search Quality
I recently had a Kagi search result that included 20 duplicate results, all from different proxy / "unblocking" domains that had scraped the same site. A terrible search experience. I was able to block those domains, but I'm playing whack-a-mole doing so. The same search on Google, Brave, Mojeek or Bing didn't include any of those duplicate proxy results. I think I have identified which external index those proxy results came from, and I would like to exclude that index for all my future results.

Helps De-Googlers & De-Bingers
Some users choose Kagi specifically to escape Google & Microsoft, and are stunned when they learn Kagi uses Google APIs to generate their results. Being able to exclude Google as an external index would help these users.

Helps Users With Ethical Concerns
Some users have previously said they would prefer not to use the Brave index. Some would prefer not to use the Yandex index. And some want access to every index they can. The politics here aren't actually relevant - what is relevant is that users can't configure their own Kagi account to work the way they want it to. Excluding specific indexes / API calls lets users ensure their money goes only to the external sources they want to fund.

Makes Kagi More Transparent
The current Search Sources page on Kagi is vague, and doesn't directly mention that Google, Bing, Brave and Yandex are index sources. Listing all the sources would help users know what is going on. It is unlikely to give any secret recipe information to competitors that they didn't know already.

Incentivizes Building An Independent Index
I actually thought Kagi was an independent index when I signed up (I misunderstood how limited Teclis is). I thought my subscription money was going towards growing a new independent service. Brave has proven it is possible for a newcomer to build a 100% independent index.

I would envision a new "Indexes" page, under Kagi -> Settings -> Search -> Indexes. There it would list all of the external indexes that Kagi uses, with a checkbox next to each. There might also be a sentence under each that briefly explains the index (eg Includes results from Google Search, and also Google Images) and with a link to the index (eg mojeek.com) for users to research that index themselves.

SearX already has something like this, in its Preferences -> Engines page, with switches next to each search engine to enable or disable:

When the index is disabled, ideally Kagi would not issue API requests to that index service on my behalf. The purpose is to ensure I'm not unwittingly funding those companies.

When new indexes are added, I would expect them to be enabled by default. Since some users may object to this, you might also need to add an option to uncheck "Enable New Indexes By Default" on that page as well.