To be useful as intended, data.ExtensionProperties needs a schema extension
If the data.ExtensionProperties block is to be searchable, it needs a schema definition, and due to the nature of ExtensionProperties (i.e. extensible information on the data block that is not known at the time of the record schema creation and assignment), that schema definition can't require updating a (possibly) locked schema definition or creating a new schema for each change.
It may be the case that proposed additions to the Schema Service and definition around virtual properties and schema extensions will handle this case.