He travels with the United States military. You act as if he travels across town to a hotel room to thank them. The idea is that as he is disembarking a plane he thanks the people who are serving. The same danger exists to the President whether he thanks his crew or not.
When the President travels, he is on a schedule and has an itenerary and a route. Most of this is held close to the vest for obvious reasons...he could be attacked.
But, he does fly into a place, and then he flies out. That landing can be observed.
Those aircraft carrying his limo and security detail also fly in and out. Usually earlier coming in, and later going out. Their landings can also be observed.
If it is known that the President makes a habit of thanking specifc crews, then a potential adversary who may otherwise not know the President's exact schedule or travel route, now can watch those crews (which may well be a lot easier than watching the President) and be preapered to act when the President comes to them.
In essence, a part of his routine or iteinerary is now "known" and enemies can exploit such information.
So, there's your example, now much more specifcally laid out for you. Agree with it or not...that's up to you.
In a time of war, I would not want to open more vulnerabilites up as regards the President.
FRegards.