"primary disadvantage" is a correct and usable phrase in written English.
It can be used to refer to the main or most significant disadvantage of something. Here is an example: One primary disadvantage of living in a small town is the limited job opportunities.
The primary disadvantage of the technique is the need for laser sources with excellent intensity stabilization.
Its primary disadvantage is the element of subjectivity which some think is not scientific.
Its primary disadvantage is that it cannot generally track averages of unbounded inputs with bounded error.
At the same time, Mr. Schwartz said, the primary disadvantage of a sit-down contract is that it costs more.
However, the primary disadvantage of participant difficulty learning how to use Second Life negated the potential benefits.
The primary disadvantage is that it can cause complications due to infections, since PD permanently attaches a tube to the abdomen.
Hence all the recommendations are about improving the characters of the disadvantaged as though these were their primary disadvantages.
The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty.
The primary disadvantages of the old system were that it allowed expenditures to be driven excessively by the burden of past commitments and to be blown off course by rises in the cost of public sector inputs.
Limited range was cited as one of the primary disadvantages of a plug-in electric car, even though plug-in hybrids are no more limited in range than gas-powered cars.
Ionising radiation and the use of potentially nephrotoxic iodinated contrast material are the primary disadvantages.
