No compost is “rich” in nutrients compared to fertilizer. Fertilizers are concentrated – sort of like “nutritional supplements” for plants, compost is “whole food” for the plants. Plants don’t just need nutrients and minerals, they also need microzhrizae, beneficial organisms, and soil structure.
Straw or sawdust is added to balance out the strong manure used in commercial compost. If manure only was used, the microbes wouldn’t be able to break it down into soil. It would become anaerobic (lack oxygen) and you would get a sludge like product, not a soil like product. You need enough brown woody material to make compost happen, but not so much that it doesn’t break down completely. With no “browns” you get a fertilizer, not a compost. Seaweed and fish concentrates are basically this.
With no dig, you still have soil. It’s what you start with, and you lay the compost on top. Even if the compost is pretty thick, veggie roots go down at least 4 feet into the ground. They will reach soil and get all the minerals they need from it. There’s plenty there because minerals stick around for a very long time.
In previous years, I added a little compost to the soil but mostly tried to maintain fertility with organic fertilizers. This year, I’m just adding a 1-2 inch layer of compost and I’m already seeing better results from my veggies than I have in years.
You can have plenty of nutrients in the soil, but if there’s not an intact ecosystem of organisms and soil structure to make it available to the plants, it doesn’t do much good. This is what compost and no dig provides. Compost may not measure high in nutrients in the laboratory, but what nutrients it does have are *highly* available to the plants.
FYI I have been using the cheapest compost I can get my hands on. Some free city compost, some cow/straw manure from a local farm. Not organic, nothing special done to it. As long as it’s not too woody and mulch-like, it’ll work.
Also be careful with liquid fertilizers. Unless you know what you’re doing, most of the fertilizer will probably wash out of the garden beds before the plants are able to use them.
How do you know if your plants are getting the nutrients they need? Watch them grow. If they are deep green, robust and growing well, they have everything they need. You can also do a soil test, but this doesn’t always tell you the whole story. Ultimately your goal is to grow good plants.