Well yeah, current FWotD is granted for whichever mode you play first. They would need to made a separate one specific to Dominion (or whatever other game mode). The idea is just to stimulate participation in the map without actually changing much at all.
Maybe they could give a double FWotD bonus to whichever mode has the least people queueing for it.
also lets not forget you can just do bot games for fwotd so it wont actually increase map populous it will just increase the amount of bot games played on a daily basis
And finally i dont think riot actually likes it if ppl can farm 150 to 300 extra ip a day
riots already nerved ip gains multiple times in the passed just because ppl would be able to just play and farm enough ip to buy every new champion that they made..this ofc makes them very little money. and they need money to keep making this game so ye ..
i don't think it will happen
unless! if they where to reduce fwotd to 50/75 ip