Are most general/family dentists capable of extracting or qualified to extract wisdom teeth unless they are impacted or have complicated roots?

Depends : Some general dentist are more experienced in teeth removal. The general dentist shouldn't go beyond his ability. He should be able to evaluate the situation and refer if he is aware that the case is beyond his ability.

Qualifications: A dental license allows the holder to perform a vast array of procedures, procedures that they are comfortable performing. Every license holder is encouraged to treat conditions that s/he feel comfortable treating. Since every practitioner is different, there is no one set answer to your question.