When people say that standing armies about centralization, what they are referring to is the development of state capacity to support a standing army.
This mostly has to do with financial matters – you need to be able to collect enough taxes to keep large numbers of people equipped, supplied, and employed year-round. However, there are also a number of other policy areas involved: logistics (even if you have the cash on hand to pay for everything, you still need to get the paychests, the gunpowder, bullets, replacement pieces for muskets and cannons, food for both humans and horses, etc. to the army on time), a more professional officer corps (granted, you still got aristocrats dominating the officer corps well into the 19th century, but the bigger armies and the need for specialized skills in units like artillery, engineers, etc. meant that you needed educated professionals as well), and so on.