You will always get disagreement when you try to change the meaning of a word when its true meaning is built into its structure. To do that is to distort logic.
A BI-llion is, by definition, a million to the second power (not to the one-and-a-halfth power as the US would have it); a TRI-llion is a milllion to the third power (not to the second); a QUADR-illion is a million to the fourth power (not to the two-and-a-halfth)....and so on.
Those who advocate the meanings in brackets are presumably happy to call a velocipede with two wheels a tricycle, a human being a quadruped, a horse a biped and three babies born at the same time twins.