I think someone mentioned this earlier, but I think the staying power of the acronyms rather than "USA soccer" or "US soccer team" is because the women's national team reached mainstream cultural relevance before the men's team did, honestly. I imagine that for a Spanish soccer fan being told the national team is in town, there's really no need to differentiate between the men and the women. "Team USA" makes me cringe, too, and in writing I prefer seeing the acronym, especially on twitter so I instantly know it's about US soccer and not a different national team.
I will root for my home country no matter what. However, when you talk about US soccer, there is ONLY 1 team... the women's. The men's team has about as much chance as a 1-legged horse winning the Triple Crown.