The five classes that I believe are near shoe-ins are, in alphabetical order:
Assassin
Psion
Shaman
Swordmage
Warlord
All of these have previously been full classes in something considered core, usually in multiple editions.
The further six that I think are warranted, again in alphabetical order:
Alchemist
Avenger
Invoker
"Machinist" (WIP name, someone who uses pure tech, not magic-infused tools)
Summoner
Warden (which can absorb/represent "Shapeshifter")
Between those 11 additions, I don't think we need any more "core" classes. There may be benefit to having setting- or adventure-centric ones, like an "Exorcist" for a ghost-focused AP, or a "Monster" class (e.g. Vampire, Lycanthrope, Mummy, Mindflayer, and Ooze subclasses) for a horror-themed setting supplement. Maybe a "Demon Hunter" for a Van Helsing themed adventure. But with the above 11 plus the existing 13, you cover so many bases so well, it's going to be hard to squeeze in anything new without stepping on toes or just reduplicating concepts.
When I'm not on my phone, I'll dig into why I think this set covers things so well.