This is one of those swings and roundabouts issues.
- On the swing - easy to enter online payment details in full without needing the physical card, easy to rip someone off if you get access to their unlocked phone running the Monzo app without further authentication
- On the roundabout - harder to enter online transactions (albeit one field), almost impossible to get access to the Monzo account unless it is your identical twin who knows your card PIN but doesn’t have your card and is trying to get access (no CVV = the need to submit a selfie using the Monzo app camera access, so it has to match the selfie you took at sign up which Monzo has on file otherwise, no access thank you)
I prefer the roundabout personally. You can always note down the CVV in code or under further authentication* using a notes/text app on your phone if you really can’t remember it or prefer to have it on your phone so you don’t need the card with you at all times. The chances of someone discovering this even with access to your phone are very slim. Freezing your account once you realise your phone is missing/nicked will probably happen quicker.
*There are apps available which provide secure access to personal information