They could give you an archievement that rewards 0 archievement points for clearing week 1. You will permanently have it on your lodestone and those archievement tracking websites if you really care about it

Tying unique rewards like titles or mounts requires to be a bit more carefull. Maybe they could give a title for clearing on the same patch as the savage release, plenty of time for something minor and bragging rights. Even then title collectors would feel pressured if they dont want to do savage or people would be frustrated they cant get it in the future etc etc...

Thats why the easy way out is just to not tie limited time rewards to anything (and why so many people are asking when are they re-releasing the old series rewards for PvP)