For some people, it gives useful visa free access to places, especially if your other passport doesn’t have visa-free Schengen, and a nice fig leaf for travel, e.g., going to Russia as a Serbian is a more appealing prospect at the moment for a US citizen for more than one reason.
I had a call with a Serbian attorney recently about a few matters, including citizenship by exception. I have business reasons to start a company there and the potential opportunity for citizenship in the course︀ of that would be a nice bonus. It sounds like Russians have driven up the︁ price of what it takes to become aligned with the interests of Serbia, to the︂ point that the outright donation option is unfavorable compared to Caribbean options based just on︃ monetary cost. The other option, involving actually forming a Serbian company, appears to have some︄ additional fees associated with it that would affect the success or failure of your application.︅ In both cases, these amounts are determined per applicant and, reading between the lines, it︆ seems to be based on how much they think they can extract. Timelines for obtaining︇ the citizenship appear to be quite short.
Naturalization has one drawback in that one must︈ renounce his other citizenships, unless that requirement is waived. It can be and sometimes is,︉ but this is not guaranteed.