The column and row reference tabs are visible whenever the table is 'active' The assumption is that if you've selected a cell, you intend to do something with the contents of that cell. Hovering the pointer over a table on which there are cells referenced by a formula on a different table whose cell you have selected, will make the reference tabs appear on the referenced table.
Deselecting the table and its cells will deactivate it and hide the reference tabs, but selecting any sell will make them visible again.
Your suggestion regarding the ability to keep them hidden seems useful. Use the Provide Numbers Feedback menu item in the Numbers menu to Make a feature enhancement request directly to Apple.
PS: The situation in your screenshot of the table with the column reference tabs in front of the 'top row(s) of the table is coused by Freezing the headers.
Freezing header rows keeps the header row(s) visible at the top of the document window as long as any other row of the table is still visible, while the body rows slide behind the header rows and out of the window.
Unfortunately, if the reference tabs are showing, they to will be kept on the screen, blocking view of the top visible body row or two, With the table not selected, hiding the reference tabs, it is still possible to scroll the sheet and the tables on it without re-selecting those tables.
Regards,
Barry