gellchom, I did include the website in the formal invitation. And every other bit of information (directions, registry, bridal party info, after party, etc.) was on the website. And it was quite clear that everyone was invited.
I think, at least from my experience, that the inserts have become so common, that this etiquette rule is one that will soon be amended. I don't know if it's just where I live, but no matter how formal or laid back an invitation (and the wedding itself) is, it has always included inserts. That is, until mine. Mine was looked at as if I was trying to cut corners by not putting the inserts in myself.
And exactly what TootsNYC said happened to me. I tried to do what was right by not including it, then people complained that I was only after cash, which couldn't have been farther from the truth.
So by not including them, I was accused of only wanting cash, being stingy on the cost of my invites, and caused confusion as to where to find my registries, and had people miss out on the after party. Like Toots said, you can't win nowadays. In retrospect, I would have rather made the etiquette faux pas than deal with all of the issues it led to.
ETA to add a sentence.