Well I was getting nicely formatted results with just [cb_point_history] but I was not displaying the field on the profile.

Query and Code fields are a bit of an exception when it comes to [FIELD_NAME] usages. They will output their template values, but they won't be ran through the appropriate layout functions or anything of the sort so it's not recommended to use raw substitutions for HTML output as this behavior is likely to be changed in a future release which would break your usage.

All I did was copy and modify /com_comprofiler/plugin/user/plug_cbqueryfield/templates/default/display.php
to table/display.php, and the same for table2/display.php.

Never modify default template files as you will lose your changes on update. Be sure to make a copy of the default template folder, rename it, then delete anything you don't intend to override in your copy.

I suppose you are referring to the class HTML_queryfieldDisplay to render the page, so the class is not unique.

HTML_queryfieldDisplay doesn't exist anymore. Please be sure CB Query Field is up to date.