Why can't a nonprofit get its own credit card?

I recently had a conversation with a NonprofitSOS reader that has been asked to be the holder of the credit card for the nonprofit where they work. What does this mean? Well, it means that a new credit card is issued for the nonprofit with both the employee's and the nonprofits name on it. It also means that their social security number is used for the card, and their credit could be affected. This also happens a lot in the business world- employees have company cards- but with businesses the likelihood of losing funding is much smaller. I recently discovered that credit card companies won't let you get a card just for the business- you have to use your social security number (I discovered this when getting a company card for The Advancement Company).

My question is, why can't a nonprofit (or a business for that matter) get a credit card with just the nonprofit or business name on it? Why does an employee have to put their credit on the line? Both nonprofits and businesses have EIN numbers (social security numbers for organizations), so those could be used to get the card. I think the main reason this happens is because the credit card company wants an actual person to put the ultimate blame on if something happens. But, I think that this should be changed- a company or nonprofit should be able to have its own credit score, which in turn would affect their rates and the amount of credit available to them.