That would be one more step that you would ask them to do instead of the time that they allot on voting day to actually vouch for their residents. It means having individual letters of attestation for each resident, which they'd have to set up, and the person would still need another piece of ID. Sometimes they may not even have that other piece of ID.
The point is that you're asking the staff to do a lot more than they already do, which is already beyond what they have to do in long-term care, as such. So, they are taking good time away from those other duties as it is. Adding that additional burden would seem to be an unnecessary step just so the whole issue of vouching can be eliminated.