It depends entirely on the child and their maturity or attitude to cycling. I am perfectly happy to let Cubester, age 11, cycle off on his own to meet his mates etc. I am also happy from watching him out on club runs that he is competent and confident, and responsible enough to lead a little group of his mates on some quiet roads and along paths etc. Cubette, his twin, is nowhere near as confident, due to a couple of unfortunate events. She doesn't want to cycle on roads on her own, and has to be very gently coaxed to come out with me at all.
I would implore the OP to take them both out and watch what they do. Does checking behind and signalling come as second nature? Do they plan ahead if they have to pass parked cars? If you spend hours drumming it into them are they the sort of lads who will think "Dad's not watching, we can revert to type?" Only you can answer that one honestly by the way!
Whatever you decide, don't become so paranoid as to end up being risk averse and passing that onto them. You owe it to them to make sure they are confident and competent for your own peace of mind, but most of all to give them the responsibility to do it for themselves.