I would prefer games worked in a way that girls have their own lives.
I agree, the "I do absolutely nothing of my life when the MC isn't talking to me" personality is quickly boring.
If the girls have a life, and this said life do not resolve solely around "being MC's onahole", then a male antagonist isn't necessarily needed. Each girl becoming then both a goal and an antagonist ; the MC will have to deal with their life and, what would be even better, understand their personality, before he can get in their pants.
As for rivals, they only really work if the story is geared for them.
From what OP said, I imagine more the kind of scenario where there's simply no story.
There a MC, there's girls, and to compensate the lack of story, there's an antagonist that also want the girls. But this, "I need to get the girls before
he get them" story is as flat as the initial, "I need to get the girls because I want it". It potentially give a reason to advance in the game, but at this level of minimalism, the same game without antagonist would be better ; it wouldn't be more interesting, but at least it would be less frustrating.
Just putting a rival in a game doesn't instantly add any interest nor does it make it realistic.
And WVM, that you named (not without reason) as boring, is the perfect example of that.
It have a story with an antagonist, but it's something that happen in parallel of the harem quest. The two are totally unrelated ; the antagonist don't care a single second about the girls, while the events due to the story do not prevent the MC to fuck all the girls he had to fuck this day. The sole consequences that the story have in the harem quest are always positive ; the MC had a reason to move into a bigger house where he'll be able to host even more of his brainless groupies, while the said groupies are even more craving to become his thing ; what by itself is an exploit.
In the end, the story parasite the harem quest, by artificially slowing it down, while the flatness of the harem quest tend to let the player disillusioned when the game goes back to the story. But well, the game can be took at the second degree, and one can simply wait to discover what will be the next Deus Ex Machina that the author will throw out of his hat.
However adding other male or female characters that potential love interests can get with if the MC doesn't choose them does interest me. That makes the game feel more realistic and "alive" if you will.
Hmm, knowing you I feel the need to complete your thought, because as it, it can be misunderstood.
This other character isn't to see as an antagonist, but more as a "second option". Not only it isn't a single character, each girl of the story having her own "second option", but also the MC isn't directly in competition with him.
Whatever if it's a friend or a co-worker, it's someone that flirt with the girl, so far without success. But if the MC isn't showing interest in the girl, or is doing to many stupid things, she'll start to see it as a potential lover. In short, it's the proof that she isn't just waiting for the MC to get in her pants ; she have a life by herself, and if the nearest person (the MC) isn't interested in her, she'll find someone else.
It can also be used as a way to make the MC speed-up his game. A simple, and totally innocent from the point of view of the girl, "Oh, no tomorrow I can't, Alan invited the team to a karaoke night. You should see him trying to sing, it's so funny", can be seen as a potential future threat ; some kind of warning, "take more care of her, you idiot, she isn't just standing there waiting for you to make a move".