[C++] Remove legacy scanner code where possible

Once everything has converted over to the non-async-generators scanner then there should be a fair amount of legacy code that can be safely removed (this is internal code so no need to worry about deprecation cycles). This JIRA mainly exists as a placeholder to mark in comments places that should be cleaned up.

**Reporter**: [Weston Pace](https://issues.apache.org/jira/browse/ARROW-18328) / @westonpace
**Assignee**: [Weston Pace](https://issues.apache.org/jira/browse/ARROW-18328) / @westonpace

_{**Note**: *This issue was originally created as [ARROW-18328](https://issues.apache.org/jira/browse/ARROW-18328). Please see the [migration documentation](https://github.com/apache/arrow/issues/14542) for further details.*}