Well, I'm sure this wouldn't be easy to implement, but it certainly isn't impossible. One option would be to make the Champion modifier class act as a middle-man for ship-stat method calls so that it can modify them as needed. Another would be to dynamically create Champion Ship Types in game as each is rolled up. There are many options. I'm sure if Keith or Chris wanted to, they could find something that would work without being too unreasonable to implement.
Not sure if this was a concern, but this option could be controlled by an AI Plot (like Avenger, Beachhead, Astro Trains, and such) so you don't need to play with it if you don't want.
@KDR_11K:
If you are playing at Difficulty 10, there is a 2% chance a given Starship is a Champion. 1 in 16 has unannounced waves (the Nightmare upgrade), giving you a 0.125% chance of getting an unannounced wave. If there are 2 Starships, 1 Golem (from a Golemite) and a Carrier in the wave (basically the only units eligible for Champion-status), there is a 0.6234% chance of an unannounced wave. That's at max difficulty with 5 potential Champion units in a wave. On average, it will happen once every 160.4 waves. With 2 AIs and waves every 6 minutes, you are looking at around one unannounced wave per 8 hours. And that assumes there are only 16 Champion types.
But if that's still too much, consider that some Champion types can be limited to certain difficulties, Champions in general can be tied to an AI Plot so you don't even need them on, and that unannounced wave could just as easily be 1/2 warning (which the Neinzul Youngster AI already has built-in) or maybe just a flat 20 seconds of warning. I'm certainly not suggesting my ideas or numbers are at all balanced. They're pretty off-the-cuff, although I don't think any are unreasonable starting points.
Planet-wide effects are good in that they make the player actually think about the situation. And when you kill the things, you've made progress. Unlike killing a Warp Guardian, which can very easily just respawn later. A specific problem Champion is incredible unlikely to respawn. And Champion structures can never respawn (with the exception of Eternal, which probably wouldn't be allowed on most structures). Each Champion creates more engagement purely because they are "over-powered" in unique and unexpected ways. You could go 100 games and never see an Eternal EMP Guardian. But you will remember that one game where he was always there to mess with you. Compare that to if all EMP Guardians worked that way by default. It would just become one more thing to deal with every game and would get old fast. In this way crazy abilities can actually be added without breaking the system when they are very rare exceptions.