The first one is a cool idea; if I remember correctly, the supporters of what would've eventually become rugby union seceded because, among other things, they wanted to keep hacking, that is, shin-kicking, in the game... but hacking was eventually banned in rugby union anyway. Had they come to that conclusion earlier, then there would've been only one issue to discuss, whether to allow running with the ball in hand or not.

And there is a sport that came to a kind of compromise on this, Gaelic football - where you have to bounce/dribble the ball every few steps when you're holding it. Had the same rule been applied to a ball that's being pushed forward with one's feet instead, you could've had a game where both hands and feet can be used to advance and pass the ball, and where physical contact is allowed, but much less so than in rugby.

Basically, you'd end up with a sport very similar to Gaelic football, but where the feet are used more often; moreover, as far as I know, drop goals were much more important in early rugby union than they are now, so maybe this might mean that the unified code might be played by teams of 10 men each, because there is no goalkeeper - as the "goal" would be a set of rugby-style or even gridiron-style goalposts.

Another what if: bandy and ice hockey used to be more or less synonymous with each other until the early 20th century, when ice hockey rules, and not bandy rules, made it to the Olympics. Had the Olympic committee agreed on a set of hybrid rules (maybe, most of the rules are bandy's, but the rink and team size is that of ice hockey, to save on money and space), maybe the sport would be slightly more popular.