Hi LudoDab
I don't know the number of messages exchanged or day but the latest I read was that 10% of all aircrafts are logging on to CPDLC. There have been numerous issues with the system but it seems that some of the bugs have been fixed recently, but the system is still very far from being reliable.
We have a list of white listed aircrafts/operators that are encouraged to use CPDLC as much as possible. Among the airlines are SAS, Lufthansa, Eurowings/Germanwings, Norwegian, BA (presently only Fans 1a aircrafts). Easyjet has the equipment on many aircrafts but pilots have not been trained to use it yet. That's also the case for Swiss. All aircrafts flying transatlantic have the equipment (fans 1a) but especially with these aircrafts the system is very slow and unreliable.
I think many of the atcos would like to use CPDLC a lot more but when the system is very unreliable still, it's not very helpful and often causes frustration when messages don't go through. Also the functionality on the atco side is very limited. At the moment we can only send a very limited number of messages to aircrafts.
Hope that answers your questions 😃