Originally Posted by mattdm
It still adds up. But I think the reason is more important: in a finished product like a web site, you don't want to expose technical background information. Exif can tell too much.
Of course, that isn't necessarily the case for the situation where the web site is
about the pictures, rather than about something else which there happen to be pictures of. But we're a) a minority case and b) the people who should know how to do something about it.

You are absolutely right. As photogs, we are generally concerned about copyright infringement and thus EXIF data is important, but there are times when you DON'T want the details of a photo known.
And yep, file size is still important, especially nowdays when we are using more and more graphic content. Keeping a lid on your files sizes in web design today is just as important. Speed is everything. The slower the site, the better chance the viewer will just get frustrated and leave.
With faster connection speed came more content. It's still important to limit the size of this ever-expanding content. Years ago, you could only include a couple of graphics or the site was too slow, so you compressed images as much as possible. Today, you can include hundreds of different graphic options. Their individual size is still very important or the cumulative effect of your graphic "package" will kill you, even on high speed. The "save for web" is still very important to a web designer...which is why it's still an option.