In my experience it is, in fact, that easy. To some extent, I would argue that it may be more or less expected. For example, geology has a particular emphasis on building a diverse background. Not so much in terms of focusing on many disciplines, but exposure to different places and ideas. As the saying goes, "the best geologist is the one who's seen the most rocks." I see that you're a geochemist, so you may or may not be as field oriented, but the point I think is still valid. Moving around will ensure that you aren't "indoctrinated" by one school of thought, experience different labs - each has it's nuances even if largely the same, and ultimately the broader your experience the better you look on a resume - especially for industry. Furthermore, the the break from a Masters to a Phd is sometime used to "refocus" your research now that you probably have a better idea of your interest than when you were coming from undergrad. Of course, if you're sitting in a top lab and the adviser and research is a good fit, moving just for the sake of moving is silly in my opinion.
I've had quite a few "should I stay or should I go" conversations with multiple professors, and really I've just parroted back what every one of them seemed to agree on.
Hope that helps