The contractor is responsible for quality, so it is a small step also to perform a quality assurance and certification function.
It is the most cost-efficient certification method - it maximises resources by avoiding duplication of effort.
The client may save on construction supervision costs.
It removes a lot of confrontation on site.
As the lowest bidder typically gets the job, financial and productivity pressures may compromise quality.
There is much reduced scope for independent checking. This may be detrimental to quality.
Some duplication of effort actually assists in achieving good quality.
Human experience is that the same person should not be 'poacher' and 'gamekeeper'.