So, remove the checks and balances that were already put in place over decades to make sure employees are spending responsibly. Um, sure.
With the employee cards, all the transactions are traceable and can be monitored with a minimum of red tape. How exactly would one improve upon that? It's literally the technologically-enabled solution.
If you want to save money and remove bureaucracy, you first create a system, then migrate to it and sort out issues, then remote the old system. Now it's going to take months to get something new in place, while also juggling manual approvals and getting things through payment systems individually.