A small inconsistency. The method by which people who have gained access to the wallet may not work if the wallet owner doesn't check the balance of his wallet or does so very rarely. I mean, he just might not know about the messages sent to him.
That's exactly the problem and that's why you can't say I will give that person 1 month/year to move their coins and if nothing happens, I will just take them myself. Maybe those are the keys that belong to a long-term storage and the owner won't be back to spend their BTC for another 5 or 10 years. You just can't assume that coins that don't move are definitely lost. Some certainly are, others are part of someone's future plans maybe.