Any objects raised from a protected wreck like Invincible need to be carefully conserved and then looked after by a museum. This ensures that the special historic, archaeological, architectural or artistic interest of the site is preserved for the nation in-perpetuity.
Archaeological excavation of a protected wreck site is often a last resort. Excavating destroys a site because you are literally taking it apart and removing objects. Archaeologists have to apply for permission from Historic England and must justify why it is necessary to excavate, for example if the wreck is be coming exposed as sands wash away.