What overhead?

Just about every web server these days supports ACME -- some natively, some via scripts, and you can set up your own internal CA using something like step-ca that speaks ACME if you don't want your certs going out to the transparency log.

The last few companies I've worked at had no http behind the scenes -- everything, including service-to-service communications was handled via https. It's a hard requirement for just about everything financial, healthcare, and sensitive these days.