I am going to agree with Cecile.
I don't see an either/or.
I started to make compost tea because I had $400 worth of plants that were dying and I didn't want to spray with toxic synthetic chemicals.
Learning how to make better compost tea was part of the process. Once you know how to make it, it's not very hard.
I have a suburban garden, not a farm, so that may make a difference.
Every year, I've been adding leaves from trees that aren't related to mine in the fall and wood chips to my soil.
I've also cultivated an intentionally diverse yard and I chop and toss- so the cuttings go under other, non-related trees/plants.
If you don't have any mulch in your yard, the compost tea is not nearly as effective. In my opinion, it is most efficient as a seed to put on other organic matter, which is what you're doing with cover crops or adding organic material.
I didn't used to make horsetail tea. Then I started to get horsetails and I've been grooving on them. My wife hates them, but I can make that tea now. I could make comfrey tea, but I just chop and toss with it.
The longer I've been doing all of these, the less I need to make compost, etc teas. Mostly it's now for plants that wouldn't naturally grow in my climate, but that I like to eat, like peaches, quince and serviceberry.
The idea with permaculture is that it gets easier over time, and you're mostly just harvesting, performing experiments, and grooving out. That's what I got.