I haven't been on the mountain very recently. However, in forty successful ascents, I never had to carry an ice axe. I think that I had one trekking pole a time or two.

Assuming that one goes up the Switchbacks or maybe has to take a few shortcuts across snow, I can't imagine the need for full crampons. OTOH, microspikes are good if you've got a thin layer of ice or hard snow. YakTrax are good if you've got softer snow.

One year we got just above the cables around Switchback #45 or so, and then the switchbacks disappeared under the snow, so we just climbed straight up the snow slope until we hit Discovery Pinnacle, which is slightly off-course.

Climbing straight up the chute is shorter, but probably not quicker. As soon as its rocks melt out, it's probably more dangerous for up or down.