I don't think we need to change 6s (or HL) to build bridges or close the gap with the casual community. The problem is simply that casual and competitive are different and they'll always be different. Even if you could play any class you wanted in 6s the strategy and mental would be completely different from casual.
Every successful competitive game allows you to play the exact same game mode as the pros, even if you're just playing casually. If a promod could allow people to play "casual 6s" in an unranked queue it would go a long way towards teaching how the gamemlde works. Then you could have a ranked queue for people who want to try a little more and get good. As players reach high ranks joining an organized league like RGL/ETF2L becomes the obvious next step. I know that was the hope for Valve competitive and that utterly failed, but I think the community could do better this time around.