If Carolina want to shed money there's much better guys to move than Faulk. If they move him they might just as well re-locate the franchise.
Staal and Skinner are only guys who makes more money. The entire rest of forward core makes under 2M and apart from Hainsey with 1 more, the entire D core makes under 1 M
Staal is logical to offload if you want to free up most money. But he is a cap dump at this point. You will have to pay someone to take him off your books with no cap coming back.
Skinner is also a guy to trade, but being he is the only offensive minded player on Canes, you just cripple your league worst offense even more
Faulk is in a spot where hed return the most (3rd overall or Drasaitl as a base)
I think you are overvaluing Falk here. His 15 ES points ranks him 65th in league for D. Under Polak and Bartkowski. His possession numbers are not amazing. Hes a 51% possession player, but so are 4 other D on his team. His CorsiRel is #1 on his team, but barely and there are 3 or 4 D extremely close to him
If you compare his numbers to Barries actually, Barrie comes out signficatly ahead. Way higher even strength numbers, similar possession numbers