It did. During the French Revolution, alongside the adoption of the metric system and the decimalization of currency, decimal time was adopted. The French revolutionary system used ten month years, ten day weeks, ten hour days, hundred minute hours and hundred second minutes. The changes to the calendar were designed to rid the calendar of royalist and religious influences, while the changes to time were simply to match the metrification of all other aspects of life.

Decimal time in France ultimately failed however, which meant it never spread to the rest of the world. First, the decimal calendar and week were seen as antithetical to the Church, particularly because it aimed to replace Sundays with the tenth day of the week, décadi. The hostility with the Church meant that most French churches never adopted the new calendar. This, and the fact that people are naturally resistant to change, meant that the old calendar remained in people's minds. There was a widespread feeling that the new calendar was artifical and pointless, particularly because anyone engaged in religion or international trade still had to keep track of the old calendar anyway. This meant that decimal time ultimately failed.

On the other hand, decimal currency succeeded because it was able to quickly and completely replace the older currency system, and metrification succeeded because it took place in other countries as well and because those who made heavy use of the metric system saw it as legitimately useful.

Source: Matthew Shaw, Time and the French Revolution: The Republican Calendar, 1789-Year XIV (Boydell & Brewer, 2011).

It did, but not in the sense of arguments over what the correct unit was. The fact is, until the 1895 Prime Meridian Conference, time zones were not widely agreed upon. I don't have the book in front of me, but the Prime Meridian was placed in cities as disparate as Cadiz, Greenwich, and Pulkova.

Beyond that, time zones would often change based on political considerations. The Philippines actually changed from one side of the Intl. Date Line to another after the 1898 Spanish-American War.

Even in the United States, various cities would hold to different times, which were often mutually exclusive.

Sources:

Ian Bartky, One Time Fits All: The Campaigns for Global Uniformity

_________ Selling the True Time: Nineteenth-Century Timekeeping in America