Why aren't oral/rectal tests of gonorrhea not included in standard std test? Don't they have complications like genital gonorrhea?

You ask/they do. The common screen for gonorrhea is done on a urine specimen. If you have concerns that you may have been exposed to oral or anal gonorrhea it is important for you to speak up. Physicians do not necessarily assume you practice oro-genital or rectal sex . Good practices require good shared communication, which is a 2 way process.