As long as the plug is correctly fused the unit should be safe.
Since if the unit surges and draws more current than it should do then the fuse will blow and the cabling will be protected. So ensure that a correctly rated fuse is installed.
Laptops and power supplies need to undergo rigorous testing to ensure that they do not explode or catch fire. The manufacturer could be taken to court if such a thing was to happen.
That said, it has happened in the past and it was with a Dell laptop.
So if your son argues then print this and show it to him:
http://news.bbc.co.uk/1/hi/business/3727…
That should be enough to persuade him.
Apart from being very bad for the environment, there are other financial reasons for not leaving it on all day, like your electricity bill.
The laptop battery shouldn't be affected by being constantly charged if it is the newer Nickel type.