It's not exactly like they had to control regions with rubber to have access to it. They could have just paid for it like we do today.
More commonly they'd just put a tariff in place, which is likely cheaper to pay for than a war and occupation.
I would note that the US struggled to produce rubber in the Phillipines, so they didn't exactly get that out of the occupation: https://www.foreignaffairs.com/articles/philippines/1926-07-...