Time is actually finite in certain situations, as well. I guess having the other players pay resources isn't a problem if it doesn't cost that much... but if the cost is trivial then why is there a penalty in the first place?
As I said in my suggestion, the cost scales with the Champion power. So if you make the "Champion" scenario 1/10, it doesn't cost anything, but the Champion doesn't make as big of an impact on the game.
On 4/10, it has a significant cost to rebuild (scaling with MK), but also is much more powerful, and has a bigger impact on the game.
At 10/10, it has a HUGE impact on the game (like a mobile Golem), but costs quite a lot to rebuild.
The reasons for a mechanic like this are self-explanatory. If you're person playing the solo Champion, you want it to have a big impact on the game. As of now, the Champion just can't do much on its own outside of nebula scenarios. It can take out maybe a guard post or two, depending on difficulty, before it dies and has to be rebuilt. On the higher difficulties it will be lucky if it can even do that.
Part of it is the novelty factor. It's supposed to be a CHAMPION
. If the best way to use it is to continually suicide it into enemy guard posts until you kill them, then that's not enjoyable at all, that's just grinding.
But what if the Champion is a powerful, 1-ship army that can take on hordes of enemy ships and wreak massive havoc just by itself? Well then it's a lot more fun to use. It's even more fun to use because there is an actual penalty for losing it in the cost of resources. You say that making the enemy temporarily stronger is a better solution because you aren't punishing your partner, but you ARE
punishing your partner. He's the one that has to defend his base and control the galaxy. You've just made that significantly tougher on him. I would much rather ask my friend to pay a specific resource cost (based on the scenario level) than to force him to defend some massive attack because of my screw-up. He can rebuild my ship on his own time, but the attack punishment is inevitable, and may come at a horrible time.
What if your Champion dies during an Exo-wave, do you really think it's a good idea to make that even worse by increasing the enemy strength?
If the players don't want to pay for a resource cost, that's fine! Just keep the Champion scenario at 1/10. I'll bet you my life's fortune though that most people are going to be playing on the higher level scenarios though, because the risk, and the power, would make using a Champion that much more engaging.