As for the "I OBJECT!" trope it normally works when the MC is being forced into a marriage, but that comes with its own weirdness since the MC needs to be literally saved from marriage so it can be a bit weird. I never liked it myself but the only time I gave it a pass and I thought it was done well was in Shrek. Then again Shrek took a stab at a lot of romantic tropes in a kind of fun way.
As for a person leaving someone on the altar, this is the way I normally understand it. The bride (because it's normally the bride) is not sure she wants this relationship or this life but is too unsure of herself to make any major decisions. The person she's having an emotional affair with is an escape. She may honestly think she's in love with the other guy, she may even genuinely be in love with the other guy or be capable of loving him somewhere down the line but his primary purpose to her is that he's a fantasy of a different life and because of that their relationship is going to be deeply flawed. She's going to build up this expectation of who he is and the life they'll have and if she does run away with him she's set herself up for disappointment. This normally all begins because the bride is uncertain, for whatever reason, and is getting cold feet but instead of having the strength she needs to vocalize her issues and try to reevaluate her situation and her marriage she decides to jump to the nearest guy to sweep her off her feet into her happily ever after and thinks everything will work out better for her. She's also selfish, she's got to be a coward for the relationship to have gone this far off the rails, but she also has to ignore everyone else's feelings entirely to run away at the altar. All the money spent on the wedding, all the guests that came all this way for her and her fiance, her family and friends who are part of the wedding party and have done everything they could to make this day wonderful, her fiance who asked to marry her and was ready to start his life with her. She considers, and empathizes with none of them before running away with her other man, to her fantasy life that is ultimately going to disappoint her.
And yeah, it's a pretty pessimistic view of the whole altar ditching trope but I've actually seen it happen personally, and every time I've heard of a friend that seen it happen there is always the same theme, the bride is selfish. And not necessarily just in that moment, but that each one of the brides were ultimately selfish people. And I think only one of the runaway brides is still currently with the man she ran away with. And the fallout of her friends and family is always pretty horrible to watch. Most people feel deeply betrayed, they thought they knew this women, some of them have been friends for years and suddenly find themselves wondering if they ever really knew her to begin with. Her family, especially if they pitched in for the wedding are furious that she just didn't call it off when she started having second thoughts and realize they raised someone selfish and cowardly. Any friendships made between the two families are tense if not ruined completely. The groom's family of course sympathizes with him and the bride's family either needs to condemn the bride to maintain the friendship and goodwill or everyone just stops speaking altogether. And the guy she ran away with in the first place is demonized by everyone. He'll probably struggle to ever maintain a relationship with her family and friends as people will project the bride's faults and cowardice onto him and try to make it seem like he was at fault and the poor bride was in some way taken advantage of or manipulated.
In short, it gets ugly, fast. The couple will be ostracised and most of their friendships ruined. Of course I've see the trope also go that the groom was either manipulative or abusive and that just adds another layer of crap to the pile and still doesn't make the bride very redeemable. She still betrayed everyone else at the wedding or they were all enablers. Plus, it doesn't make the whole running away with another man trope more romantic. She's just trading situations and is still being saved by romance which is a problematic trope in and of itself.
The healthiest way I could see the trope happening is if the bride started getting cold feet, realized she was latching onto another man as an escape but actually respects him, the groom, and herself enough to call off their relationship and the wedding. Does some soul searching and they end up together somewhere later down the line after she's happier with herself and her circumstances. She'll still be a little demonized but she'll still be a respectable person for having the courage to stop things before they got too far. However, if you decide you want to go with the literal left at the altar version that's also fine. It comes down to it being an internal conflict with the bride (or groom should you decide to swap the genders) that she's made external through her own personal character faults and as such her redemption needs to be handled carefully. She's both the antagonist and the protagonist of the situation and she needs to battle with her own faults and misconceptions. She doesn't need to be this caricature of an evil woman of course, you can make her realistically flawed. The women I've heard of that left the altar, some were very much like disney villains and others were just weak willed women that really, really needed to grow a backbone.
But, regardless, this is your story and it's important to do it the way you want to do it. It's okay if some of your stuff is a little problematic or tropey. I assume everyone else is like me as well and we write, ultimately, what we'd love to read. If you want to do it a certain way, then do it that way. I understand things like twilight and 50 shades are inherently problematic but they still have a fan base. Its up to those fans to make sure that they don't internalize those problematic aspects, and it's up to the creators of those things to make sure that we don't present problematic things to people who can be hurt by them (minors and other influential people), but it doesn't mean we must be 100% non-problematic. (It's probably not possible anyways.) As long as within the realm of your story you call out problematic things as being problematic and don't frame problematic things as being totally romantic and good then it won't be a problem. At least, that's how I see it.