The problem is how to verify those certificates. As an example from the BBC "about 100 people are trying to enter England each day with a fake negative Covid certificate. Lucy Moreton, of the Immigration Services Union, which represents UK border and customs staff, told the All Party Parliamentary group on coronavirus that the documents are "very easy" to forge." Asked how many fakes could be slipping through the net, Ms Moreton said it is "inherently unknowable", adding that a lot of border and quarantine controls are based on "trust".
Also not all vaccines are created equal - just look at Chile. Which ones do we accept - which ones do we not?