You just listed seventy-one 'Tec appearances. Mostly of six or eight pages. Compare to 127 issues of 22 pages plus another 200-odd pages for the minis and specials that preceded the series. And that's not counting BATGIRL, AZRAEL, BATMAN, DETECTIVE, CHRONICLES, CONFIDENTIAL, GOTHAM KNIGHTS, LotDK, NIGHTWING, or SHADOW OF THE BAT, or any of the innumerable minis and one-offs or crossovers that she played a significant role in, or JLA.
Which is all before we get to guest appearances.
There's no "may" about it.
"Influential" is a different matter, and entirely beside the point. The Anti-Monitor is extremely influential and important to DC; he's the lynchpin around which CoIE turned, the symbol in one single character of an event that defines the entire genre of superhero comics. Nevertheless, you're not going to see him have a lot of girlfriends, because all the influence and importance in the world doesn't give him any more pagetime than he's got, and his pagetime ain't enough to really explore the operatic drama of his lonely antimatter heart.