It’s kinda sad, but I’ve concluded that terminal capabilities that require a custom TERM are not worth it. Why? TERM is one of the few environment variables that are passed to remote systems by ssh. Unless you’re in a position to ensure that every system you access has a terminfo entry for your custom terminal name you’ll experience brokenness.
These tools — terminal emulators, shells, SSH, etc.— derive a lot of their power and utility from universality. It’s best to embrace that, rather than fight for local customizations. The way to get italics in your terminal is to update terminfo upstream and wait five years for distros to pick it up. :-/