I am not sure of the choice your company made, as it is one of the main advantages for employees to have an automatic feed for not entering all details and for the company to keep an eye on the spending avoiding in addition double expenses.
In 2007, on my first implementation, we started without having a card implemented, but we did within a few months... I never heard the opposite way (from having a corporate card to not having one). My assumption is that maybe the card provider now was giving inconvenient service so I would have look other providers.
In all cases, if may help, you could still have individual feed into concur by registering your personal card, if you and other employee wished: