Some disagreement here
"but just as we feel confident sitting them in front of the TV before nine..."
The TV is not a babysitter. Do things with your children, sure watch TV with them, but don't dump them infront of it. As for the "confident" bit I assume that you have never accidentally strayed up into the channels 900+ on Sky, and no child has ever watched their parents putting in a four digit PIN on 12 rated films before the watershed?
"so we should be able to log them onto the internet without having to look over their shoulder the whole time"
I would suggest having the PC in a public room into which you randomly wander, noticing a panicked ALT-TAB or whatever should be pretty obvious. Or if you like having a router log and every Sunday morning you and the children go through every website accessed by them so you feel a part of their world?
"(which limits their freedom in other ways)" care to list three? Why is everyone else's freedom to be curtailed just to make you think your kids are not looking at smut? Note the word "think". We have all grown up, and while this makes life a little more difficult for them somehow every generation has found a way to look at pictures of naked people. THIS WON'T HELP FOR MORE THAN AN HOUR. Once the first kid at school learns how to circumvent it, every kid in school will know. In my day we had jazz mags at school from the kid whose dad owned a newsagent, there will just be the electronic equivalent.
"becomes impractical as the number of children increases)." Your choice to have more kids than you can deal with, not mine. Why should that inconvenience me to get back some websites that will inadvertantly get blocked (and some will, witness notes on Flickr and Tumblr above).
"As for the idea that ISPs, and by extension the UK government, will get a list of those who like porn that makes no sense. " Citation needed. It makes perfect sense, imagine Percy Dribblemouth is accused of child molestation. Added in will be the prejudicial "AND he wanted porn on his laptop." It makes as much sense as the Government wanting to record each and every internet dealing each of us have. Luckily that makes no sense either, oh wait...
Responsibility for what your children do online, or offline vests with parenting. They are your children, and your responsibility. Just because you can't be bothered to parent them, or you don't trust them (now, who is to blame for a lack of trust), does not mean that every other soul in the country has to be inconvenienced.