In the cool season, I would certainly agree, but not in early June. On June 1 the average high is 99F at Phantom Ranch and it is 100F by June 4 (and well over that as the summer progresses).Second, a Rim-to-River-same-Rim is about the effort of middle difficulty 14er: 14 miles, 5,000 feet and class 1 trails (the outer trails have class 2 scrambling). Crossing rims is longer, more like 21 miles or a long 14er hike like San de Christo in one day or Longs.
99-100F may not seem that hot, but when climbing uphill for hours in the sun it can be brutal (and 100F is just an average; it can be way hotter than that). From a physical standpoint rim to rim in early June is going to be way harder than climbing Longs Peak, assuming you do Longs in non-technical conditions.
Of course a rim to rim day trip can be done then (and many people have done it), but it will be harder than climbing a 14er, at least for most of us. One plan many do is to leave early in the morning, soak in the creek throughout the day and hike back out at night. It would be much better than trying to hike out in the afternoon.
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Despite the fact that they are easy trails, far more people have died on the Bright Angel and Kaibab Trails than they have on any mountain in the United States. In fact, the seemingly benign Bright Angel and Kaibab Trails have killed more people than Denali, Mount Washington, Mount Hood, and Rainier combined.
Just use common sense and you should be OK.