Meant also to say I have a copper beech with a TPO on it since long before we lived here. If we want to do anything with it such as lopping or trimming in any way we have to apply for permission to the council first.
Having a TPO on it won't stop him "accidentally" damaging it and will cause you endless hassle if you want to trim it or remove it in the future. It will also make your house a little bit harder to sell.
When my mum was selling her house which has a large copper beech tree with a TPO, one of the couples actually said that the tree was putting them off putting an offer on the house as it would be too much trouble! Never caused my mum and dad any trouble in the 30 years they lived there, but each to their own.