Here's a very simple but functional head to head game which many people who have played it have said is fun:

Blurb from the Multimorphic website:
"Heads Up! is the first internet-connected game for the P3. Play against an opponent on another P3 in the same room or anywhere in the world! Heads Up! creates a shared playfield across two connected machines, presenting the exact same targets to both players. Shoot green gem shots, and you score points. Shoot red portal shots, and your ball goes to your opponent, allowing them to rack up more points. It’s simple in concept but layered in strategic complexity. As shots are made and missed, the gems and portal shots change state. Master the timing to maximize points!"

https://www.multimorphic.com/store/p3-game-kits/heads-up/

Well, one of the major problems with pinball has always been the fact that multiplayer play is turn-based. The famous Gottlieb slogan is "it's more fun to compete" but in pinball when you compete you have to wait around, hoping your friend will drain while you wait for your turn. The P3 solves this with networked head-to-head and multiplayer play. Internet connectivity makes this even more attractive, because you can play with anyone, anywhere in the world.

You asked for an example of a functional and fun head-to-head game and I gave you one. I'm sure Gerry and the rest of the team would agree that Heads Up! and Cosmic Cart Racing are just a start but they open up enormous possibilities. Maybe it hasn't made much of an impact in the pinball hobby yet but new people and kids at shows love it and it has also had success on locations which have a high percentage of casual players. This is the demographic that pinball needs to appeal to in order to grow.