I like the E-Wedding idea as an OPTION. For example, "We're having a destination wedding and you're more than welcome to attend. If, however, attending will not be possible for you, please consider attending virtually!" I can understand (and even get behind!) that type of scenario. If it's "Hey, we're getting married, and we don't really want you to come, but we still want to 'invite' you so you feel obligated to get us a gift," then I'm not okay with it.
As per the gift "rule," I've never heard of that, nor will I ever abide by it. I give what I can. For my brother's wedding this past month, I gave some cash (not a lot, but some) and made a gift that is traditional in our family for the bride. Normally my grandmother would have made them, but she passed away early last year, so I did it. So, I guess what I'm saying is that even though I didn't spend a ton of MONEY on my brother and his wife's wedding gift, I think I gave something more important. What can I say? I don't think money should be the central focus of something like that. :)