I believe Barclays can scan the cheque from the app and processe it. It would be good if Monzo could offer something like that instead of posting.
Hi Chris & welcome 
The HSBC app has also had cheque imaging for a while now and it works really well!
As far as Monzo is concerned, it has sparked quite the discussion for several years and there are no official plans to support it at this stage (it was announced that it wouldn’t be developed a while ago)
The main thread, if you have the stamina to go through it, is here;