I've worked in a few teams that called themselves Agile. In each case, they were approximately so in various respects, drawing on various elements variously strictly.

The main disadvantage I've seen is where the talking to (prospective) users is very separate from the development effort, the developers seeing only the stories that are now or next on the roadmap. Having an understanding of the technical detail that's coming down the pipe in much later sprints can heavily inform how earlier stories ought to be implemented and that foundation can be expensive to adjust once built on.