I think we need to stop and define what "coming out" actually means, because your question seems to be based on a bit of a Bridgerton-induced misunderstanding. To come out was simply to be declared an adult who could participate in society and, perhaps most importantly, be courted. Preferably, this would be marked with a ball or other social event held by a young lady's parents or guardians, but all that was really necessary was an agreement that she was "out". A young lady who wasn't out wouldn't accompany her family to balls and assemblies or participate in a ball at her home, so if they allowed her to attend, it would be a clear sign that she was now to be considered out even if her debut wasn't strongly marked.

We can see the different shades of this throughout Austen oeuvre. The only book in which coming out really plays a role is Mansfield Park, where Fanny begins the main narrative as not out, and is permitted to come out as the "queen of the evening" at a ball held by her uncle for herself and her brother. It marks her as eligible for marriage, which is exactly what her uncle wants as he notices that Henry Crawford pays her some attentions, and would like her to be ready to receive them as courtship and eventually marry him.

As for the ball, so near at hand, she had too many agitations and fears to have half the enjoyment in anticipation which she ought to have had, or must have been supposed to have by the many young ladies looking forward to the same event in situations more at ease, but under circumstances of less novelty, less interest, less peculiar gratification, than would be attributed to her. Miss Price, known only by name to half the people invited, was now to make her first appearance, and must be regarded as the queen of the evening. Who could be happier than Miss Price? But Miss Price had not been brought up to the trade of coming out; and had she known in what light this ball was, in general, considered respecting her, it would very much have lessened her comfort by increasing the fears she already had of doing wrong and being looked at.

(Mansfield Park, chapter 27.)

When the carriages were really heard, when the guests began really to assemble, her own gaiety of heart was much subdued: the sight of so many strangers threw her back into herself; and besides the gravity and formality of the first great circle, which the manners of neither Sir Thomas nor Lady Bertram were of a kind to do away, she found herself occasionally called on to endure something worse. She was introduced here and there by her uncle, and forced to be spoken to, and to curtsey, and speak again. This was a hard duty, and she was never summoned to it without looking at William, as he walked about at his ease in the background of the scene, and longing to be with him.

... In a few minutes Sir Thomas came to her, and asked if she were engaged; and the “Yes, sir; to Mr. Crawford,” was exactly what he had intended to hear. Mr. Crawford was not far off; Sir Thomas brought him to her, saying something which discovered to Fanny, that she was to lead the way and open the ball; an idea that had never occurred to her before. ... Sir Thomas smiled, tried to encourage her, and then looked too serious, and said too decidedly, “It must be so, my dear,” for her to hazard another word; and she found herself the next moment conducted by Mr. Crawford to the top of the room, and standing there to be joined by the rest of the dancers, couple after couple, as they were formed.

(Mansfield Park, chapter 28.)

At the other end of the spectrum, in Northanger Abbey nobody actually talks about Catherine Morland coming out directly. She is a poor-ish clergyman's daughter and as such, her parents aren't going to throw a ball in her honor. The fact that her parents allow her to go to Bath with the Allens and dance and visit there is all the sign there is that she has changed her social situation.

If a family disapproved of their daughter for some reason before she entered society, they could potentially not throw a ball in her honor, for her to open the dancing like Fanny Price in the place of honor. This would be neglecting to "launch" her. A presentation at court was not a usual part of coming out, it was something only available to the upper echelons of society, and unlike in Bridgerton, it was not a parade of newly eligible ladies: it was just a ceremony where all sorts of people would be introduced to the queen and be able to attend court later, if they wished. The larger efforts shown in Bridgerton to "launch" young ladies like Daphne are done specifically to make them more marriageable. The more balls they attend, the greater chance they have to catch someone's eye and make him initiate a courtship; the more importance they seem to have within their family and the more money spent on their social debut, the better they look to potential husbands (who are always considering dowry and connections while evaluating future wives).

So, not "launching" would mean vastly decreasing the chances of the daughter/sister getting married. This could perhaps be seen as an effective punishment for a problematic young woman, but it would also punish the family by forcing them to continue supporting her and failing to create a new social connection through her marriage. It would also be highly irregular for any younger sisters to come out if she were still not out, so gossip could severely damage their chances and their family's overall reputation. (On the other hand, if the young lady in question were a younger sister of an unmarried woman, delaying her coming out indefinitely with the excuse that she needed to wait for her sister to marry would be acceptable, up to a point. It was not a rule that only one sister could be out at a time, but there was a sense that older sisters should get their time in the sun before potentially being outshone by a younger sister, as marriages were generally supposed to occur in birth order.)

I am not aware of any examples of young women being prevented from being considered out due to their family not liking them.

Such instances were rare enough to be hard to find. It’s more common to find stories of ‘gentlewomen’ who did marry, and then left their husbands. Upper-class women tended to marry young, and knew perfectly well that they had no access to money or support without their families. Check out the subsection in this paper on consent theory as it relates to the position of Victorian women.

Married women had a little more freedom to meet people and make discoveries about themselves, so there are many instances of women at least attempting to remove themselves from marriages they found distasteful. This could get tricky if children were involved. The case of Caroline Norton is a famous illustration of the challenges women faced in leaving the fathers of their kids. Norton’s activism led to the establishment of some limited protections of women’s rights to custody of their children.

Caroline Norton’s granddaughter-in-law, Lady Grantley, provides a well-documented case of a young childless woman who left her husband and remarried.

There are more visible instances of disownment among the middle classes and minor gentry than among the debutante class. Elizabeth Barrett Browning is one well-known case. She was disowned by her father after he learned of her marriage to Robert Browning—when she was 40! The thing about such disinheritance is that it wouldn’t affect a girl’s social debut, because it would occur after she began to socialize and meet men.

A parent who did disown an adult child would not be required to acknowledge or support them. It’s only since 1975 that disinherited adult children in England have had significant success in pursuing shares of their parents’ estates, due to the Inheritance Act of that year. Previously, the testator’s declared intentions were regarded as more nearly absolute. However, debutantes were typically minors, so parents were required to support them and had the right and legal duty to control them. Controls included chaperonage, physical restraint, and the authority to refuse consent for marriage. A young girl who misbehaved was far more likely to be confined than disowned.

Some social launches happened after marriage, either because a girl was married early or because the groom’s parents had necessary connections that the bride’s parents lacked. Presentation to the queen required an application sponsored by a lady who had been presented herself, a kind of gatekeeping that surely kept the numbers under control. So a mother-in-law might make the application. By that point, the bride was out of her father’s control and in the hands of her husband and in-laws.

Finally, a debutante’s come-out, if presentation to the queen was required, was only possible with the queen’s consent. If a girl or her family became non grata at court for social reasons, that aspect of social launching would not be possible no matter how much family support the girl had.