The ParserOutput has a getProperty and setProperty method
https://gerrit.wikimedia.org/r/#/c/244379/ demonstrates how the RelatedArticles extension can work without CustomData.
What else uses CustomData is there a unique problem it solves or should we look to sunset it?
AFAIK, this mainly exists because setExtensionData() wasn't available. As a 3rd party developer, I have used it and then switched away. However, it does mean that in quite a few cases, we have to implement onOutputPageParserOutput to get information from ParserOutput to OutputPage, which CustomData does automatically.