I think that's been part of Torts shuffling lines, Briere wants to evaluate how different players fit different roles before giving extensions and the TDL. I think Tippett being comfortable on the left side probably played into the decision to extend him - has more value if he can play both sides. Foerster has also played well there, impressive for a 21 year old rookie, to both break into the NHL and do so on his off side.
That's an important part of rebuilding, if they were serious PO contenders, they'd trade a RW for LW to balance lines rather than experiment to see who can play on their off side. Same on defense, playing Sanheim at RHD, etc. Some players are comfortable on their off side, others struggle. Knowing what you have tells you what you need.
I think Briere would love to see Michkov move to center, just to get a read on whether that's an option down the road. But no control over that situation.