WotC put this out a little bit ago as part of their 5.24 previews. WotC is advising certain "complexity" levels to each class, and I think its worth looking at what they are thinking is complex.
(NOTE: Everything is speculative unless you have a 2024 PHB and are breaking NDA. Keep in mind we don't have a full picture of the scope of rules and ability changes yet).
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So the first thing I see is the the pure martials (fighter and rogue) are Low complexity. I would certainly say the Thief and Champion are. On the Other Hand, bard, sorcerer, druid, monk, and warlock are all High, which I think is again is fair. Bard's magic secrets are going to be very tricky and require knowledge of four different spell lists. Warlocks are highly customizable with invocations, sorcerers juggle two different resources (SP and spell slots), druids need the monster manual to run, and monks are another resource-dependant class. I would generally agree most of the rest are average, though wizard as average is certainly a choice (I get sorcerer and bard both need a lot more understanding of the rules, but wizard isn't exactly easy to run either).
I imagine most people will have differeing opinions on the complexity, but assuming there are only three levels, I kinda agree. I would call wizard High and I think Ranger is teetering on Low, but otherwise think this correct.
Wizards are harder to level and hard to build, but IME they are not actually that complex to play once you have that done.
IME Wizards are easier for new players to run in play than most fighters in 5E. In 2024 I think they will be easier than most Fighters or most Rogues given the complexity added to the Rogue class. So I don't really agree with that list at all.
If you are playing a game with new players and a bunch of pregens Wizard is not really overly hard at all. Bards, Sorcerers and Druids are all substantially more difficult than Wizard. Clerics are about the same generally (some subclasses more difficult), Paladins are more difficult, Monks are more difficult, Rangers about the same, Barbarians it depends entirely on subclass. Warlock can be very easy or very difficult depending on what Evocations, pack and subclass you put in it.