Good answer Jaba. I certify engines on-condition and it is really the accessories that need the careful inspection and consideration.
I am a firm believer of 'On-Condition' engines.. at least you know what you have got.
I have seen figures like you spoke of, from memory it was something like 6 times more likely to fail in the first 50 hours after overhaul compared to keeping it in service.
You can play with the figures any which way of course... I will post a few links here to some of the American views on it.
The Savvy Aviator #4: Debunking TBO
The Savvy Aviator #45: How Risky Is Going Past TBO?
The Savvy Aviator #48: Reliability-Centered Maintenance (Part 2)
The carb and mags really need to be in good condition, - no engine will be reliable if you have adverse wear in these components. Given that the components are serviceable then the engine should be able to continue in service subject to satisfactory completion of the On-condition check list.