Consultation first. Every couple can learn something from meeting with a clinical geneticist. They evaluate both family trees & can identify genetic issues you may be at risk for. With this information they can focus on which if any conditions to look for. There are in excess of 200 gene related defects they can identify, but there is no test that will identify all & many are studied only in a couple labs in the US.
Impractical at this. Time for general screen. What would you test for? If there is a family history of an illness, e.g., huntington, tay sachs, cystic fibrosis, it may be appropriate to test both partners. There are too many genetic markers associated with diseases to do a general "genetic test". With reduced cost of whole genome sequencing, it may become feasible in the near future to perform such analysis.
Agree. The 'SHOULD" part depends upon ones religious or other beliefs. Individuals who want to know before conceiving and want to do something about it if the get a negative answer are the ones who should be tested. Otherwise it will cause undue anxiety, and may also effect their health insurability. .