The people most likely to make mistakes as to when this gear is supposed switched into and out of; therefore, it makes sense to have and use the prescribed gear. I believe people who are clueless to the actually risks should not take the short cut you suggest. Anyway, what's BD Raven ice axe weigh? Less than a couple of pounds? If you are not prepared to carry 20+# for a day hike this time of year, you really should not be on this mountain.
Also, neither you nor I know what the conditions will be in late June. I do know I have used ice axe and crampons later than this in the Sierra after big winters followed by cool springs.
