This is exactly how I use Synchi! Same idea but I use Logseq instead of Obsidian (very similar open-source alternative, worth checking out). Works great for syncing markdown notes between computers and my phone on demand. Of course I need to remember to sync before switching devices, but I prefer this then constant running in the background.
Haven't thought about an Obsidian/Logseq plugin but honestly that sounds like a great idea... For now it's CLI only, but I can definitely see the value.