Are you suggesting that "periodically" and "from time to time" are synonymous?
I guess I'm saying that they can be used synonymously, not that they always are. (But what should I know? I've only been speaking English for over 60 years.).
Could that be an Americanism?
Could be. A native BE speaker would need to provide input as to such a usage takes place in BE.
AHD also includes the "from time to time" sense (and, unlike M-W, says nothing about "frequently"):
1. Having or marked by repeated cycles: periodic oscillations.
2. Happening or appearing regularly or from time to time: periodic dental checkups; periodic rain showers.
3. Characterized by periodic sentences.
Note that "regularly" and "from time to time" are separated by "or."