I think one of the reasons that quick bowlers don't often get the captaincy is that they generally field at fine leg or third man and are therefore too far away from the action to lead their team in the field. Southee fields in close most of the time, sometimes in the slips, so he wouldn't have that issue. I think he could do it. He's belligerent and seems like a leader, which are both positive attributes obviously.
Kane is so vital to our batting lineup that I'd be very hesitant to put more pressure on him or give him something else to think about, but lord knows the kid can handle pressure up there with the best of them, so maybe that's a bit unfair. Who knows, maybe he'll step up to the plate yet again - like hitting a 6 to win an ODI against Aussie when we were 9 down and wickets had been dropping like flies.