I'd keep the main four, not because they are traditional but because they all represent distinct and useful archetypes. The least useful is Cleric, being a character that barely exists outside of D&D-influenced fantasy. Still that is a lot of fantasy nowadays.
Then I'd keep Bard, Warlock and Druid, because they are all also distinct and useful archetypes which have grown to have strong identities (stronger than Cleric I'd argue, in some ways).
Rangers have never had a solid identity and can be easily done by picking specific skills as a Fighter, or multiclassing, or as a Fighter subclass. I love Paladins but they could easily be a Divine Fighter subclass without losing flavour (they might lose some cool mechanics of course). Barbarians are even more indistinct than Rangers and again a Fighter subclass which had unarmoured combat and Rage would do the trick. Hell maybe even lose Rage - Barbarian and Berserker seem like different things to me. Sorcerer is a solution in search of a problem, and could be rolled into Warlocks in many cases. Metamagic is weird and doesn't sit well with post-3E D&D. I could see dropping the Metamagic angle and making Sorcerers and Psions a single class with a spell point mechanic, which would fit well with a lot of literary fantasy characters. Monks are distinct but always a weird fit and seem like they might be an option for another class (perhaps a generalised Mystic?) than a whole thing.
Of course, dropping nothing is my preference. More classes are better than fewer with D&D-style mechanics, but those are what I'd pick.