I asked my mortgage advisor who told me if I’m asked for paper statements I should provide them for every account I have. I think those lenders who do like to see statements wouldn’t be too happy getting one from my legacy bank which shows a proportion of my salary (all the spending bits essentially) going to 
Monzo without being able to see where (and on what) I spend my money, as this is essentially why they ask to see statements.
The lack of paper statements is probably the last stumbling block preventing me from switching fully over to Monzo, as I renew a mortgage next year and intend to begin to sign back up for paper statements ‘just-in-case’ from January.