Of course, here in the 21st century, there is little actual reason for our Congressional representatives to go to Washington in the first place -- they could easily caucus, debate, and vote electronically. But then they would have to stay in their home districts, and be held accountable for their votes by constituents at the grocery store, dry cleaners and the service station. And none of them wants that!
Eggggs-zackly! Video conferencing saves Corp-America a lot of bucks, and I can even partake right here with my web-cam, a high-speed link, and some software. I've 'sat in' on meetings with a dozen other folks!
Our congress critters, tho', would miss their 'perks', fab lunches, dinners, and Happy Hours.....
....and they'd have to, as you point out, mix with us 'common folks'.