The major reason for this is that there is no better way to measure a country's economic health. Try to think of some other way to measure this and think of the problems.
If you go by employment, that's not such a great measure. A country could have 100% employment, but have all its people employed as street sweepers and people who carry things from place to place, things like that. Their economy would be worse off than an industrial economy with 10% unemployment.
If you try to find some measure that would solve some of GDP's limitations, you have trouble too. Let's say you want to include the value of work done in the home. How are you going to measure the value of me taking care of my own child? Or the value of me cooking meals for my family?
So the thing is, other measures have problems that are just as serious.
Anything in the world is used primarily because of its capabilities, and not because of its limitations. GDP is no exception to this rule.
No doubt GDP has many limitations, but at the same time it has many advantages also. In addition there are no other convenient measure of total economic progress that can totally replace GDP. Finally GDP is required even for deriving many other economic measures such as per capital GDP, and GDP in terms of purchase power parity, that may be used used in place of GDP for some purposes.
Major advantage of GDP is that it is simple and convenient to measure. In addition being one of the earliest measure of economic activity to be developed, it is widely used, making it the most commonly available measure of economic activity. Further, it is very simple to ascertain with no subjective or judgemental elements. Further, other measures that may be used to replace GDP are also not free of their own limitations. Finally it is the starting point for determining economic activities in terms of many other improved measures of economic activity and well being.
Thus GDP, in spite of its limitations, is still a popular and useful means of measuring economic activity and well being, although it is being increasingly being replaced or supplemented by other indicators of economic activities and health.