Why not make International Timing Zone just a straight line like this?
The main reason why the International Date Line doesn't run down the 180° meridian as you have suggested is because all nations determine their own standard time zones, applicable only on land and adjacent territorial waters of that country. This date line is not based on international law, but on national laws. The International Date Line is simply just an artificial-construct decided by cartographers.
This means that any country near the date line can shift their national time to either side of the International Date Line if they wish to. There have been several historical examples of this occurring, such as when the Republic of Kiribati gained independence and acquired new islands as a part of its territory across the International Date Line. Obviously no nation wants different parts of its territory running on different dates so the government of that country will choose unilaterally to change their nations time-zone how they see fit. This creates the zig-zagging International Date Line we have today.
Though, it is worth noting that in international waters time-zones do follow the 15° wide longitudinal lines as you have suggested as being ideal.
You may find this link useful:https://en.wikipedia.org/wiki/International_Date_Line
In a perfect world the international date line would run directly along the 180 degree line of latitude. The reason it doesn't is due to the borders of Pacific island nations. No nation wants to have the eastern part of its country have a different day to the western part of its country just because of an arbitrarily drawn line on a map.