I've been to Philmont twice. Once as a Crew leader in 2011 , once as a crew advisor in 2015.
It really depends. Is your crew doing a big "peak bagging" type trip where your crew is doing 80+ miles? If they don't care about the program at the next camp/camps they are hiking through, then a wake up time is not as important.
If your crew is really keen on doing a certain activity at a camp they are staying in/hiking through then they need to consider what time programs generally end at philmont (I want to say it's 4 pm but I could be wrong...they also need to consider there may be a line...) Most backpackers generally walk between 1 and 3 miles per hour depending on the terrain, weather, temperature. Depending on the section of philmont that is something to important to consider. Breaks are another thing to consider. With a crew your group is generally going to be taking breaks. This depends on again on the terrain and weather.
I would sit down with my crew leader and navigator at night and ask them questions. "Do you know where we are going tomorrow?" "What route are we taking?" "How long do you think it will take us to get there?" "What activities do you plan to do?" Based on that, they would decide when we needed to get up. The earliest we woke up on my 2015 was 5:30 AM. That was the day we hiked up Baldy Mountain, which has a time restriction on how late you can begin the summit.
Unfortunately, with stuff like this, there is no perfect answer. It's always some flavor of "it depends."
One thing is for certain, your Scouts will love Philmont.