I don't use them myself, but I think a reason they become used by people is because neopronouns don't typically have any preconceptions about them. More often than not, one is entirely unfamiliar with them or have only heard of them. Traditional pronouns, like she and he, often have gendered preconceptions with them. For example, I go by she/her precisely because most people would make the (in this case, correct) assumption I'm a woman from that. Otherwise I don't really have any particular reason to go with she/her over they/them or even neopronouns. And even they/them can have preconceptions about it, such as it being entirely gender neutral.

Also, fun fact: the first recorded English neopronoun is "thon" from the mid-1800s. So even neopronouns are not exactly that modern. Though, they are recent in terms of how old is English is.