magento2 – Magento 2.4.2 cacheable search results (past first page)

We have seen that Magento after first page (whenever there is a p request parameter) the code forcibly makes the page un-cacheable.

Is there a reason for allowing the first page to be cached and not the rest?

The code in MagentoCatalogSearchControllerResultIndex:105-11 removes the “q” parameter and then if it sees any other parameter it flags the results as non-cachable.

We wish to enable caching in search results (all pages) but wish to be sure it wont break anything.

(we use varnish)