When they say that it is not necessary to brief a normal take-off, I think they mean that your 'standard profile' does not need an indepth explanation every sector. So if you take LNAV as standard above 400' and take climb thrust and accelerate at 1500' as standard you don't have to go through all this. Just say standard T/O. If however you are going to do something different, like HDG SEL at 400' and take climb thrust at 1500' but not accelerate until 3000', perhaps due to a restriction you need to make, then brief that.
As pointed out by others, the important differences must be briefed every time, like emergency turns, MSA and plan if you have an emergency (will you return to this airport, which might be the 'standard' thought process, but what if it's a limiting runway? You may well want to fly 50nm to a 10,000' strip of the black stuff!) Tell the other guy your plan, brief the bits that are different.
Hope this helps.
PP