First, nothing in Sec. 508 specifies table summaries.
Second, Sec. 508 specifies the international accessibility standards for digital content, such as WCAG and PDF/UA, and it's the accessibility standards that state whether tables need summaries or not.
Most tables do not need table summaries. The summary element is an outdated requirement from back when screen readers were very primitive and couldn't announce how many rows and columns were in a table. That hasn't been the case in the past 10-15 years.
However, Table Summaries can be helpful (brief summaries, that is) when tables are complex: that is, they have multiple headers, spanned and merged rows/columns, or how the data is presented might be confusing. There's a short but good explanation from the W3C at https://www.w3.org/WAI/EO/Drafts/tutorials/tables/summary/
So today's accessibility guidelines do not require table summaries: they are optional, and more times than not totally unnecessary. If you think a table needs a summary, then the table needs to be rebuilt or reformatted into a better, more accessible table that is readable by all users, not just those who use one brand of screen reader.
Summary:
Whoever is requiring that ALL tables have summaries is nutzo and needs to upgrade their understanding of today's technologies, standards, and guidelines.
You won't find any tool in MS Word for table summary, but you can try to use Table Properties / Alt Text to meet the need. The "description" field will be carried over into the exported PDF and placed into the Alt Text attribute of the Table Tag.
But don't expect it to be voiced by screen readers because most don't recognize Alt Text on tables and the feature could be disabled by end users.
Table Summaries were deprecated in HTML 5, mainly because if that type of information is needed by those using screen readers, then it most likely should also be available to all users, not just those with vision disabilities. Remember, Alt Text and Summaries are announced only by screen readers (some screen readers, that is) and is hidden to all other users.
References:
WCAG 2.2 (released October 2023) is here: https://www.w3.org/TR/WCAG22/ and its matching techniques are here: https://www.w3.org/WAI/WCAG22/Techniques/
WCAG 2.1 is here: https://www.w3.org/TR/WCAG21/ and its matching techniques are at https://www.w3.org/WAI/WCAG21/Techniques/
—Bevi
US Delegate to the ISO committees for PDF and PDF/UA
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