I don't actually agree with that - well, at least not unless you are doing your character all by yourself and looking at all the options.
If you are helped by someone, and they realise that you are the type who prefer simple options, and steer you to the appropriate essentials class, then it is reducing complexity, as you don't have to deal with a class with a higher complexity.
Likewise, if you are a beginning player, and just buy an (or both) Heroes book, it is reducing complexity by a) offering you less choices than if you looked at all the books; and b) offering classes with less complexity.
So, ironically, Essentials adds complexity to the system by adding different options that work differently, but also reduces complexity by offering characters that are themselves (for the most part - the mage is about as complex as PH characters) less complex. That said, I think where it matters it reduces complexity - because for those who it matters (who want less complexity) will not be canvassing all the options anyway.
Take, as an example, my friend's wife. He's been trying to get her to play D&D, but she's been reluctant. She has never played any RPG or wargame. He has played the D&D wargame (not Ravenloft, the other one like it named after a red dragon), and she liked it. Now, if he were to get her to start D&D, and suggest a slayer instead of a barbarian, how is Essentials, by providing a simpler option, adding complexity for her?
For me, arguments that Essentials is more complex strikes me as similar to arguments that early Macs were harder to use than DOS - sure, that's true if you are the type who wants to program in options, but for those less computer litterate that just want to type up a letter (the consumers for which it was first intended)... no way.