It's not just web sites that do this. When you open the Twitter client on Android, for example, it'll go to the top of your feed instead of to the tweet that you read last, forcing you to scroll down, reading tweets until you find one that you've seen before.
Well I wasn't even talking about syncing across devices but yea - that Twitter behavior pisses me off. They also show me the same unread notifications on every device. The frustrating thing is that I know how easy it would be to fix.