I do not mind having to show the card, but I do mind being told that we do not need the car unless we are at a land border crossing or I think the CBP Officer specially called at Immigration and Customs in St. John USVI and then having to show the card to be able to access the machines.
Have a consistent clearly defined policy about the use of the card, something like it can only be used for Immigration and Customers Purposes at Land Border Crossing, but you should have it with you to prove that you are eligible to utilize the service at all other locations.
I can only speak for myself, it is not hard to carry the card with me, but it is annoying to be told that I do not need the card but then I am asked to show it to be able to access the Global Entry machines when I am specifically told otherwise.
Of interest I finally heard back from the MIA Airport regarding the line organizer wanting to see the Global Entry card and the Line Organizers were having lots of trouble with people seeing long lines, seeing a shorter line and assuming that they could use that line as well, even after being told that line was for Global Entry Only, thus for a short period of time they were asking to see Global Entry cards to prove eligibility to access the Global Entry area and avoid the long line for regular immigration.
She said once they were alerted to the fact that one was not required to have their Global Entry card on them to be able to access the service, they removed that restriction and a verbal acknowledgement of being part of Global Entry was enough to be allowed to bypass the regular line and access the Global Entry Machines.