Competition? Well, not everyone accepted the Gregorian reform. The Julian calendar remained in use in the Russian Empire until the Bolshevik Revolution. The Russian Orthodox Church, as well as other Orthodox churches, continue to use the Julian calendar. For example, Christmas is on January 7th.

I'd say that the "consolidation of power" happened during the period of colonization led by Western Europe. In many instances, Western Europeans put themselves at the top of a society. So official business, documents, etc. would be done using the Gregorian system.

There are countries that use different systems. For example, Japan still uses the system of counting years according to the amount of years the current emperor has been in power. Japanese know the Gregorian system and are well aware that it is now 2015. However, for most if not all official documents the current year is Heisei 27.

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