Same experience here in India. Larger companies (with $billions in revenue) pay in 1-3 months. Small/medium companies pay in a week.
The problem is that in big companies, nobody really owns anything. So you're going to have to chase a whole bunch of people and processes, from finance to compliance to HR. And it's not individually any single person's fault.
You seem to suggest the paying-late is a symptom of the org, my experience is different : I happen to know certain big corporations have departments making sure bills are paid as late as possible, including haggling the invoices down.
Paying late is corporate finance 101. Or at least 201. I remember building spreadsheets in class showing the difference in paying bills on time vs net 30, 60, 90. The difference is pretty significant when dealing with large numbers.
The difference used to be significant when inflation and interest rates where in the order of 10% year over year. It's not the case anymore since they dropped to near zero, unless you really don't have the cash on hands to pay now.