We're always open to improving the docs sites, so thanks for the suggestion. In the specific case of Algolia's offering, there are a few issues that make it less attractive than what we're currently using:
1. Cost. Algolia's starter plan is a very good deal. However, as we add supported versions of OpenShift Container Platform to the docs site, we could easily approach and exceed the records and operations threshold for that service level. The next jump up is considerably more expensive than what we currently pay for Google Custom Search.
2. Static site integration: GCS easily shims into our static docs pages, which contain very little scripting. On page load, the search code is dynamically loaded from a static shim. While Algolia offers a library for plugging their search capabilities into a Jekyll-generated site, the documentation is thin when it comes to loading their necessary forms and scripts directly into page templates.
I'm sure that someone could pull together a plausible proof of concept to address #2, but the cost issue is still a factor.
Regardless--thanks for putting this idea out there. Google Custom Search is certainly not the only search product out there and if we can find a better offering that satisfies the issues that I described above, then we should definitely continue the investigation.