Are GRE/GMAT or other certificates needed for academic career after PhD?
Good GRE and GMAT scores will make it easier to be accepted into the graduate program of your choice. They will have no bearing on post doc hiring decisions

Similarly language testing is used to ensure that English problems will not prevent you from being successful in graduate school. Once admitted your language skills will continue to improve during your studies and your TOEFL scores will no longer matter.

The only exception to this would be if you want to work for a test prep company that trains student for the GRE, GMAT or TOEFL. Ignoring this possibility, your testing results are not important after you are accepted by the University and begin your studies.