As of July 14th, there were at least 2 significant snow fields that need crossing. And they will be there for another couple of weeks. For some, both can be done butt naked while drinking a beer, for the vast majority, it will require a better sense of confidence. I understand that the 18 inch wide path carved by the thousands of boot steps, looks navigable but think about it this way.. Depending on the time of day it will either be icy or slushy. Both circumstances would benefit from some kind of traction device. If you're going to attempt these traverses without crampons, then at the very least you should have micro spikes with an ice axe or trekking poles to help balance your naive attempt at surefootedness in these conditions. However, if you slip and begin sliding down a 40 degree slope (60 degrees at the top of the chute), good luck trying to self arrest with trekking poles. This is why an ice axe is the way to go when you're dealing with a scenario that may require you to self arrest. I know I know, an ice axe is another piece of equipment to lug along and at 18 ounces, yes ounces, it's just too much to carry. But when you slip and you start sliding down a 100 foot slope (at the meadows) or 1000 foot slope (at the top of the switchbacks and down the chute), if you survived and are injury free, you now have to ascend that section all over again. And from the top of the chute, that's at least another 2 hours and more than likely will ruin your summit attempt. When you stab your ice axe into the snow, you instantly feel in control and that makes all of the difference in the world. Use some good judgment and take an ice axe with you until the snow fields have melted away. They can be rented in town for $15. If you're concerned on how to use an ice axe for self arresting, below are two links that will serve as primers which will give you the basics for the conditions you will likely come across this month. Practice these easy maneuvers on some easy slopes at the meadows or at Consultation Lake. It will serve you well. Be safe and don't leave your wag bags or trash behind!
Side note: I wore my micro spikes and used my ice axe for confident stability. I also had my trekking pole with a wide basket on the downhill side for the snow field at the top of the switchbacks while using my ice axe for the uphill slope. If you plan on getting to the top via the chute (a much harder approach), then you would absolutely want the ice axe.
One last thing: Don't try glissading down the chute. The snow is too shallow and you'll be busting your ass and breaking bones for 1,200 feet. If your feeling the itch to try some glissading, the slope at the cables is a much safer alternative.