You'd think that huge things like the 456 and Miracle Day would have a big effect on his (current and former) companions and their families.
If the Doctor picked up an American companion from, say, March of 2002, would you expect him or her to talk about 9/11 a whole lot?
People can go through things that are traumatic on a societal level without it absolutely traumatizing them on an individual level.
As for whether or not the 4-5-6 Crisis would affect the Doctor's companions...
Well, none of his post-Series Four companions really coincided with the Crisis. His adventure with Christina in "Planet of the Dead" apparently occurred the year
before most of Series Four, if I remember correctly. The next time we saw him, he had landed in the year 2059 on Mars -- the 4-5-6 Crisis having been 50 years passed. He landed next in Christmas 2009 London, and the crisis was already over -- and, frankly, it's not like the Noble family have any children themselves. But it's also obvious that British society is hurting in "The End of Time, Parts One & Two," too.
The next time he lands in "The Eleventh Hour," he first lands in 1996. When his five-minute trip lasts twelve years, he ends up in 2008 -- a year before the crisis. Finally, at the end of "The Eleventh Hour," he finds himself in 2010 Leadworth, two years after most of the Atraxi crisis and almost a year after the 4-5-6 Crisis.
As for how the 4-5-6 situation would have affected his newest companions.... Amy and Rory had no children, and Leadworth seems to have few children in general. It's possible that none of the children selected by the British Cabinet for enslavement by the 4-5-6 were anywhere near Leadworth and that as such, the British Army never entered their village. (Remember, Prime Minister Brian Green's government specifically decided to target children from under-performing schools and economically disadvantaged families for enslavement, not a general 10% of the entire child population.) For Amy and Rory, the 4-5-6 Crisis may well have been something horrible that happened and they can't believe it, but still something that happened Somewhere Else and not something that personally affected them.
