Hazrat Omer ra did not change the status of Tarawih, he merely asked people to pray in one jama'at instead of small gatherings.
The whole argument id laughable at best. Its not bida'a if you do a Sunnah or a Nafl daily, that was done by Prophet pbuh once in a while.
Well if you feel like that then I am sure you don't mind disproving the fact that it is bid'a.
I have given proof that it is from Hadith, feel free to provide the proof that it is otherwise.