The key thing with TSB was that none of their thousands of employees could fix the problems for weeks in end, so it appears many customers have come to the real

The key thing with TSB was that none of their thousands of employees could fix the problems for weeks in end, so it appears many customers have come to the realisation that they should not be with a bank that cannot rectify issues, and thus they are looking elsewhere. You seem to be trying to signal that you're conservative. Thus in this scenario, you would leave TSB and go to another established bank with thousands of employees - and maybe, despite their legacy systems, you'd be fine. The original person in the example though has reached the point where they're leaving and they're willing to try something new. They won't actually be at greater risk of loss, since there's a well established ombudsman and UK banks have a guarantee (FSCS), so then it becomes a matter of inconvenience from any bank mistakes (until they're rectified) and the level of features - with modern systems, it's entirely likely the startup app-only bank will do better on both these points. So it's not the sort of gamble you seem to think it is after all...