Maybe you would care if that website was yours. These attacks do not discriminate. If your Wifi connected lightbulb (just writing that makes my eyes roll back) is part of a botnet, one day, it might just take down something that you actually need.

That said, them being connected to the internet isn't an issue itself. Make all your IoT devices connect through one central gateway (in your house) that controls all of them and suddenly instead of 20 devices broadcasting on the internet you have a single entry point. Obviously this entry point would be the target of many, many attacks, but securing this one gateway (that would be easier to update than your lightbulb.) is much less of a complicated task than securing all twenty.