Googlebot or Less-sophisticated bots are even more likely to get confused by relative links, even under typical circumstances. The only way to ensure that you've eliminated these uncertainties is by utilizing absolute URLs, and doing so consistently across the site.

More at Yoast Why relative URLs should be forbidden for web developers

Relative links specified in canonical tags are a terrible idea, as they violate the very purpose of the canonical tag: disambiguation. Always, always specify canonical URLs in absolute form, or don't use the canonical tag.

If your staging site is publicly-accessible on its own, you definitely don't want to be using relative URLs in the site navigation links (menus, footers, etc.) because even a single incorrect link deployed to production can open up the whole staging site to being crawled, indexed and returned in search results. The potential implications of having multiple copies of your site in search results are difficult to understate, and range from wasted crawl budget, through duplicate content issues and UX confusion, to serious security concerns depending on the setup.

If your site publishes RSS feeds, relative links appearing in the feed content probably won't work, so inline links in content should always be specified as absolute URLs. They also help to deter all but the most sophisticated web-spammers from republishing content their spambots have scraped from your site.

Image search can also benefit from specifying absolute image URLs by asserting ownership in the image search results, thereby reducing duplicates from competing sites, particularly in cases where they're hotlinking to original image content on your site.

http://www.dirigodev.com/blog/seo-web-best-practices/relative-vs-absolute-urls-seo/

But with WordPress' absolute urls you end up with insecure image warnings on them.

Not if you search/replace and make all your images and your site url and home urls https. Which you should.

There's no point in me repeating all that.

A 'valid' reason?

Plugins. By keeping them absolute, we allow plugins to more easily and efficiently filter images and redirect them for things like srcset in a dynamic way.

Also it remains easier to move, and portability of owning ones own data is a major selling point to WP. Sacrificing that would be a bad move.

I understand that WP's target audience is not true software engineers, but in my 10+ years in developing software, I've never heard a valid reason for an absolute url unless it is for an external resource.

What are your valid reason for using them?

It will take care of the serialized data as well.

This is a must have tool for WP dev.
https://interconnectit.com/products/search-and-replace-for-wordpress-databases/

Thanks Interconnect