Well, I think Enki actually introduces academics earlier than Waldorf. Enki grade 1 is definitely aimed at 6YOs and there is plenty of reading instruction in Enki grade 1. Waldorf doesn't usually start reading until age 7. I have seen recommendations from people using Waldorf to guide a child who has an early interest in reading into other activities.
That said, we all have a journey within any interest we take up, be that natural family living, a specific educational model, etc. Early in the journey we may see things one way, and later that may have changed. It doesn't even necessarily change in the same direction for each person; I know people who were adamant about delayed academics come to a place where they think that following the child's lead is best, and I know who wish that they had delayed academics.
Once upon a time I thought that they best way to use Enki was to adopt it as a lifestyle. Not that I think that makes a lot of sense if one hasn't read the Enki Foundation Guides, and really what I would have meant was seeking to establish a strong base of rhythm, environment, and health and to seek to meet the child's developmental needs.
Eventually I came to realize that not only could I not *do* Enki just as it was presented in the guides, no one else could either, and the creator of the Enki philosophy and method had never intended for it to be a box to live in. What a relief!
The change in me was realizing that there is no perfect way to do anything, and no way to do everything perfectly. There is no reason to get trapped in methods and dogma (this applies to everything , including unschooling). A lot of what you find in the various holistic educations methods doesn't have strong science behind it; I personally don't believe my child is incarnating into this world (a Waldorf idea). I think wet-on-wet watercolor is lovely, but I don't think my child will be scarred for preferring tempura paints. I don't believe that my child will forever have a brain imbalance for not having learned to knit in grade 1.
I think people who develop educational philosophies and methods look at the world and see things that they think could be better, and they think the way to do this is through education. They all have some great ideas, and some clunkers. What they say will resonate with some people, and not with others. People who develop educational models are not gurus, and I can tell you that the creator of Enki Education doesn't see herself as one, doesn't want to be one, and really doesn't want people to be dogmatic about Enki.
If you want to use Enki fairy tales (they are lovely!) but never want to do a movement circle, have at it! If you want to use Enki sage stories with Saxon Math and a classical approach to history, more power to you! If you want to read the Foundation Guides and get a rhythm going in your home even though you are 100% sure you will be an unschooling family, what could it hurt? You may not win a popularity contest with those who use Enki more traditionally, but it really doesn't matter if anyone else thinks you are doing it "wrong". It only matters what you think and how your child(ren) responds.
There isn't a single person writing homeschool curricula today who knows your child(ren) the way you do. They take the old models and the old ideas on child development and psychology, combine it with new research and their own observations, and try to make something new that will be relevant to a large group. Some are more successful than others. You are the only one who, together with your child(ren), can figure out what works best for you as a family.
I'm currently using some of the Enki philosophy and methods, but no Enki resources at all (my boys are past the grade levels that Enki has available). We largely unschool (although I hate labels, and we're unradical), and I grab the parts of Enki that I need when the boys express a desire to learn something. (You want to learn division? Great. Let me see how Enki teaches that and whether or not it makes sense for us. Does that look like fun to you? Great! It doesn't? Okay, let's see what else is out there.) I also use classical and Waldorf resources when they work for us.
Enki is a really great program, and is certainly the most family-centered homeschool curriculum I have personally seen. I would hate for someone to think that it is an all-or-nothing curriculum, because you could miss out on parts that would really work for you.