Does every single table in a thesis need to be numbered?
If the tables are not referenced in the thesis text, why are they in the body of the thesis?

I'd put them all into an appendix, number them, and provide an appropriate, terse label.  If there are specific ones that are referenced many times in the body of the thesis, you should include these in the body. Duplicate the in-body tables in the appendix.

If all the tables are in an appendix, there is no need for an index of tables, but it would depend on the norms for your subject area.