I think the main reason is that United Staters is really a mouthful, and neither of those words by themselves is very descriptive, whereas "America" a least narrows it down to a single hemisphere.
The other inhabitants of the Americas are of the opinion that we (in the USA) picked this term ourselves (which is debatable) and that it is emblematic of our self-centered and egotistical nature (they have a decent point there). So when speaking or writing in a forum where there are liable to be folks from the western hemisphere outside the USA present (particularly people from Latin America) it is a good idea to avoid saying "Americans" to mean USA residents. I have seen people angrily set straight for doing that.
As an alternative, the Brits like to use "Yanks". I don't have a big problem with that, but many southerners wouldn't like it, as that's close to the perjorative term they use for the northerners that beat them in the US Civil War. As mentioned in the comments, you often see USAsians online these days. It's clever and I like it for written works. However, when spoken it sounds so much like "Asians" that it could be confusing.