In FR's case over 90% of pax check in online and have a printed boarding pass. Stiff penalties (£55 per person) have ingrained this to the traveling public. Closing online check in 2 hours before departure allows more headroom when reselling seats and estimating loads.
Those with a bag to check-in are already indirectly paying for the use of the airport check in desk, and it also takes less time/administration, albeit only by a few seconds.
Charging for online check in will simply lead to lost revenue, as the vast majority would still be happy to check in at the airport (for example, TUI flights), and extra overhead due to having to employ further check in staff.
Revenue from missed online check in penalty + saving on airport staff costs > Revenue from online check in fee + paying for more airport staff.
Those checking in online, printing a boarding pass, and hand luggage only don't even to need to interact with staff until boarding. Encouraging people to check in the airport (by charging to check in online) will only unwind that process.