For me, doing regular soil tests and reapplying the needed minerals on a regular basis that make up “fertilizer” is a common occurance. Animals grazing the fields or removing crops from those fields takes the nutrients away. Land always needs “a bit of help” with added nutrients to be very productive in growing a crop or pasture grasses.
I am sorry to tell you that applying a layer of compost now and again or a bit of lime is NOT enough to help the land produce even grass well. The minerals get unbalanced, providing great habitat for many kinds of weed, items that you don’t want to grow.
As for the Nitrogen, sawdust does NOT deplete Nitrogen from the soil, per my local Fertilizer Agent. The Nitrogen may be “tied it up” a bit longer breaking sawdust down, but actually"'never is gone" from that soil. So at times some extra product for Nitrogen is needed to help keep the plants going well, plus lime to free up nitrogen already down in the soil for plants to use more easily.
I get a substitute for Urea, which adds the needed Nitrogen, but is not harmful to the equines grazing those fields. Substitute cost almost the same, so no extra costs when I fertilize. I do try to fertilize yearly, using soil test results to put on just what is needed to grow good pasture. You can fertilize in early Spring or early Fall, works well in both times in my location. I don’t do “Natural type” fertilizer like the free chicken or hog poop on my fields. That stuff does tie fields up longer in breaking down, getting evened out in balance of the field, than I can have on our small acres. Potent to the point of harmful for quite a while, even disced into the dirt.
I do spread the sawdust, shredded wood stall bedding on our fields daily, it really helps our soil get added organic matter down into the clay dirt. As with any organic product, the fields need more bedding to be constantly reapplied, since it breaks down all the time. Does last longer in the soil than straw bedding, which we gave up years ago. Now there is only straw used if we have a new foal planned. All those little organic particles keep the clay soil open, aerated for good drainage, easier root spread by the plants.
And what is wrong with adding commercial fertilizer in recommended amounts to the land? Not overdosing so the extra stuff washes into the water table, but putting on what the land needs is good husbandry in farming. You sure can’t expect fields to constantly supply good grazing, new crops, if you only take things off them and never add anything like fertilizers. Compost is neat, helpful, but seldom high enough in needed balance of minerals the field must have to produce well.