I (over)think about this kinda stuff all too often, so here's some loose thoughts:
As others have stated, there's the similarity between inflation and erections, but there's also something fulfilling about the feeling of "fullness". If you wanna get Freudian, you could argue that the desire to be inflated/"full" could be to compensate for the physical/emotion distance between the subject and their mother/their mothers' breast, which could also apply to inflators, since the inflation process is a method of immobilization, of converting your desire and affection into something that physically changes them, brings them closer to you.
I read a great book a while ago by psychologist R.F. Baumeister that shed some light on the objectification angle of the fetish (and similar fetishes), the book is called "escaping the self" and it's an investigation of all the methods that humans develop to escape from the 'burden of selfhood', from alcoholism, to religion/spirituality, to suicide, and masochism. The investigation of masochism ultimately concluded that through the endurance of physical punishment and pain, there's a numbing effect, which takes our minds away from the awareness that we're independent beings with histories, ambitions, and wills, (supposedly, zen buddhists might disagree...) and towards the return to the safety and formlessness of being unborn, where - going back to Freud, you're safe inside the mother. Relating this theory to inflation, it could explain why some are compelled to inflate themselves IRL, not only because it simulates the afformentioned feeling of "fullness" and "fulfillment", but because the physical feeling of being stretched out simulates immobilization, bringing about this physical numbing. Paired with the belief that you're just a balloon, no longer human, there's a kind of private (albeit, obviously fleeting) comfort that comes from that, considering the constant pressures of being an independent person existing in public in the 21st century. Likewise with humiliation, when you consider the amount of work that one has to put in to comply with the societal rules of not sticking out too much or drawing negative attention, it makes sense that the inversion could become a sick fascination, the thought of being the center of attention, of being too huge to ignore, drawing jeers and teasing from the crowd. Indulging in this public humiliation fantasy is almost paradoxical: on the one hand, you can safely, privately, cathartically indulge in the "forbidden" while reinforcing your own continued public compliance with these standards - you can (privately) have your cake and (publicly) have it, too.
As for why this fetish is more common now more than ever, there's a lot of reasons. Returning to Baumeister's theory, you could argue that our society is more public than ever, increasing the burden of selfhood, which encourages people to find more avenues for escape. There's also the fact that visual media is unprecidentedly omnipresent in the first-world, especially for young children. Innovations in film and video technology make simulated fantasies not only more hyperreal (compare the SFX in '71 Wonka to '05 Wonka) but also more private and reproducable; wheras in the 70's you could only see 'fetish fuel' in public places like the movie theater or TV, hoping to maybe see reproduced stills in magazines or comics if you were lucky, now we can rewind, we can watch clips online, we hoard and trade fan-made fetish content regularly on mongolian fur trading forums like the one we're on now. There's no longer just a screen in town that you have to share with your neighbors and strangers, no longer a screen in the living room you have to share with your family, but countless screens in the bedroom, in our pocket that we own individually. With this privacy and intimacy, we can continually re-live whatever fantasy we want, thereby reinforcing the fetishistic fixation of your choice (whether or not it is a choice, or just chance).
As for why people tend to get 'stuck' on a certain fetish, I think a lot of it has to do with the capability to reproduce and reinforce the fetish through repeated interactions with online media, as well as the seemingly insatiable appetite of human sexuality. In other words, when our brain finds a way to consistently and conveniently reap pleasure, the pathways that link stimuli to rewards get formed fairly quickly, and can only become more plastic when the reward diminishes (which is why some people can find themselves 'acquiring' more fetishes over time, chasing the high).
I think socialization plays a role in this as well, which might explain why a lot of people with this fetish tend to be on the spectrum (though it could be a case of vocal minorities, ofc, and the whole identity politics of autism is another barrel of monkeys entirely...). Nevertheless, people who are considered to be/identify as being on the spectrum tend to be less susceptible to social pressures than others, tend to repeat/replay things habitually, and tend to be more physically sensitive, perhaps making suggestions of bodily transformations feel more intimate, believable, and appealing.
TL;DR we live in a society; your mother, and sho on and sho on...
P.S.
I'll acknowlege that my knowlege of Freud is pretty surface level, I definitely think someone with a deeper understanding could draw a more compelling connection between the body transformation fetishes and the death drive, but I don't understand it enough myself to comment.