I always considered it a major part of the franchise
Funny thing is that DOA2 and DOA3 was when Team NINJA was toying with making the game exclusively a tag game. It was due to DOA2U's online success where the data showed roughly 9 out of 10 matches done online were solo matches. So they changed course from there.
Plus there's the whole thing where having twice as many characters cost twice as much RAM which meant stages had to be downgraded from their potential/solo counterparts.
My theory is that I think it was a combination of those two points, with the additional point of difficulty in keeping both solo and tag balanced, attributed to their decision.
I'm personally of the opinion that tag will return in the future I'm sure, but maybe as its own game a'la the Tekken Tag Tournament series. I also feel that VF x DOA could one day happen where they could use the existing Tag system as a base in its own game. Of course, these are just pipe dreams of mine.