Should you manually ping new WordPress posts?

This is one of those things I tend to call “ritualistic”. Search engines will never explicitly tell you either that pinging does anything or nothing at all. It’s there for them to use or do nothing at all about.

From my experience semi–active WP site with basic decent SEO setup (such as sitemaps) would be scanned daily anyway.

If your content is extremely (to the hour) time sensitive you could consider going extra mile to make sure about pings to relevant services. Outside of that it’s not typically (in my experience) something that time gets spent on.