First of all, I hate the title of this trope, because it's not a true triangle. It's a V, with one person being the love interest of two people who they have to choose between. A true triangle would be if person A likes person B who likes person C who likes person A. But it's far too late to try to change the name of such a well received trope, so I guess we're stuck with it.
Anyway. In a love "triangle" *sigh* one person has to make a choice. The most common sequence of events that I've seen in love triangle dramas is when the center person is already dating someone and a new person comes into their lives that they are interested in. Do they stay with the person they're already with, or do they dump that person and go with the new person?
My first instinct is to say: go with the new person. If you were really in love with the first person, you never would have noticed the second. That seems the easy answer.
One of the ways I've seen the drama build is when the central person can't think of a good reason to break up with their current partner. That person hasn't done anything "wrong" per se. They're just not the right person. But if you realize the person you're with is "wrong for you", that should be a good enough reason to break up with them. Yes, you're probably going to hurt their feelings, potentially even break their heart. But you're not doing them any favors by staying with them out of shame or pity. And you're doing any favors to the person you want to be with by avoiding that relationship.
Worse, sometimes these dramas will have the central person actual cheat on their current partner with the new love interest. Please, please, please break up with someone rather than cheat on them. They will be far more hurt by the cheating than you breaking up with them to be with someone else. And the person you're cheating with probably feels like crap, too, being the side piece and all.
All that being said, I have written love triangles a time or two, because they do feel so realistic. This is something that people face out here in real, 3D life, so it should be reflected in fiction as well. In one romance, I did an unrequited love triangle, where the central person stays with their current partner because they never developed an interest in the second person who was yearning for them. But in the other story, I had the central person make the switch, and it was a very angsty moment for him, which is always fun to do to my characters.
I feel that this trope is definitely a standard for a reason, and will remain as such. I just wish it was named correctly.