I think you'll find that is exactly what people do. However, payroll solutions are highly customized for every individual company and even business unit. You don't buy a payroll software in a box, deploy it, and now you have payroll. Instead, you pay a payroll software company, they come in and get information about your payroll systems, and then they roll out their software on some of your systems and work with you to make sure their customizations worked etc. There's rarely any truly "off-the-shelf" software in B2B transactions, especially the type of end-user solutions that also interact with legal systems.

Also, governments are typically at least an order of magnitude larger than the largest companies operating in their countries, in terms of employees. So sure, the government of Liechtenstein has fewer employees than Google overall, but the US government certainly does not, and even Liechtenstein probably has way more government employees than Google employees in their country.