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Reflections are a bad mechanic in general, both in teams and one v one, because we don't have much of the historical counters anymore (mass passives). All for nerfs. They were on my list too.
That said, the champion strat doesn't work against champion teams, because you have two choices: deny faith or deny yourself starbursts. If the enemy team is champion and you get burst, you lose champ, then they get faith on the true kill. Slightly mitigates, but not really a solution (unless you're all inhumed or something).
Hmm, some thoughts:
+1 to outpost changes and efficiency deletion.
You could switch those research affects with attunement. People would capture obelisks for those, none of the attune affects are that great though. I think part of the big desirability issue with the current system is the best shard skills are the ones you get for free, not for holding the obelisk.
The problem is if its not doable now for recovery missions it won't be doable for offensive missions. If its not doable for offensive missions, there's no point.
To put this in perspective, I didn't even starburst in that. Cyr never truedied (he burst once). The offensive team died in excess of 25 times. Noone is going to want to do this when the defence can literally curbstomp you with minimal effort.
To be fair I think we've seen how things pan out pretty well. Antioch alone has done at least 10 raids just against Kinsarmar, and all but three were heavily contested. I don't think its accurate at all to say that raids only happen when everyone is offline.
Not to say timezones aren't an issue, but we've definitely seen both sides of things in the raids that have been going on.