having just came back from patagonia.... some thoughts for you
1) approaches entail mellow trail, followed by things like endless moraine, scree, steep moraine, glacier travel, steep bergschrunds, snow/rock glisadding etc.... Its hard to find a shoe that is optimal for all those conditions. As with everything in climbing, skill and technique increases your margin of error.
2) honnold and caldwell did the traverse in very dry conditions. Things are not always that way. For different conditions/different routes, anything from a tennis shoe to a full on alpine boot are appropriate.
3) wouldn't recommend leather-based shoes-- they take forever to dry.
Popular options that I saw were the Salomon X Alp Carbon 2 (if not planning to do any ice climbing routes) and the lightweight scarpa ribelle boots. I also saw a lot of people using running shoes for the initial parts of approaches, then switching to bigger boots once in the true alpine.
best,
matt