First there will be those people who assumed it did already. There are ads online, how can an advertising standards authority not be looking at them? It's logical enough.
The other set of eyebrows to be raised are...well...mine. And what surprises me isn't the idea that the ASA isn't monitoring adverts, it's the idea that any single-country and therefore parochial organisation could even begin to patrol the Internet when by definition it exists without geographical boundaries.
This is where it gets very difficult indeed to see how such an idea would work. I'm from the UK, which makes me linguistically close to America but psychologically I believe I'm closer to Europe. This isn't a political but philosophical statement - you might remember the famous 'nipplegate' incident in 2004 when Janet Jackson's breast was partly exposed during the Superbowl; over here we don't all know what a superbowl is, any more than Americans would be expected to identify the FA Cup, but it hit the news mostly because everyone was so surprised at the fuss. You want to see topless women, you come to many mainland European beaches in the Summer - but it's no big deal. One of our national newspapers, the Sun, has a topless woman every day on page 3 and it's considered a family newspaper (I confess I find that a little odd).
I mention this example because I don't want to draw in more extreme moral mores from countries with which we have other disputes; this sort of mis-match between two cultures as closely allied as the UK and US would make it difficult, I suggest, to reach consensus every time over what's acceptable and what's not. Come to think of it you'd probably find difficulty reaching true consensus across every American State.
I'm torn, I admit. Should there be some sort of moratorium on violence, Nazi images, explicit sex, to market products and services? Yes of course there should, because if there isn't then a tiny handful of organisations will seek to take advantage of any laxity. But can I conceive of how you'd put the right watching organisation in place? Unfortunately not. Any suggestions welcome...