Grass fields can get torn up easily, especially if the ground is wet. This also can make for dangerous playing conditions. A synthetic surface does not have this same drawback. It is much easier to prepare a synthetic surface than a natural grass field. The field will maintain consistent quality throughout the match. Maintaining a natural field is expensive. Introducing an artificial field would make it possible to have a nice clean field to play without the heavy grounds-keeping required.
In the 1970's artificial turf took off in many outdoor sports due to its perfectly groomed appearance, ease of care, and the fascination with anything that was man-made replacements of nature. In the 80's that fad wore off and many sports returned to the natural grass.
The biggest disadvantage is probably the occurrence of turf toe. However, modern shoes and improved surfaces reduce the risk from the early days.
Typically with turf toe, the injury is sudden. It's most commonly is
seen in athletes playing on artificial surfaces, which are harder than
grass surfaces and to which cleats are more likely to stick. It can
also happen on a grass surface, especially if the shoe being worn
doesn't provide adequate support for the foot. Often the injury occurs
in athletes wearing flexible soccer-style shoes that let the foot bend
too far forward.