I'd be pretty surprised if it went that route as any business passengers that maybe loyal to Frontier will jump ship. Companies will reimburse pax for the first checked bag but not carryons, leaving the pax having to foot the bill on that without reimbursement permitted.
On all the major network carriers and Southwest, JetBlue and Virgin, there is no charge for a carry on.
Spirit charges for carry-ons but Spirit doesn't want business pax. It wants Delta and American to charge double for a route like LGA-DTW, while it flies the route under the radar and the legacies don't price match it.
Since Frontier has a DEN hub and might have some business pax in Denver that have chosen to fly Frontier as it's carrier, a fee like this would pretty much wipen their base of business pax there.
I don't think it's ready to go in full leisure mode like Spirit or Allegiant.