WooCommerce & No Indexing Shop Page

Hi to all,

We use WooCommerce for several sites and wanted to know if anyone has had any experience or recommendations on setting the shop page to no index.

The reason for asking is that the shop page displays all products on the site, its not categorised, just displays all products from newest to oldest and we don’t see this being a page that we want users to click on as there is no logical format that products are displayed in other than new to old.

If we set the shop page to no index, will this do any damage to SEO?
SEMrush

I am thinking that all products are categorised and google will be able to follow category links to get to all products. If Google crawls all categories and the shop page, they are using up our crawl budget by scanning the same products twice.

Any comments?