No, it's not just for the nitrogen content, which is usually pretty low by the time the composting process has taken place (fresh manure should never be used on open ground, it needs composting first). Adding humus rich, or organic, material such as composted manures or garden compost (produced by anaerobic means or not) to soil increases the bio diversity within the soil, and usually, trace elements - more bio diversity means more nutrient availability for plants growing within the soil. Humus rich materials are a 'catch all' prescription - they help poor, thin, sandy soils, and also help heavy, claggy soils. Soils which constantly produce crops and which are never treated to the addition of humus rich materials become poor and thin - the chemical fertilizers used to feed the crops growing within that soil simply provide nutrients to the crops, but do nothing at all for the soil. And it's the soil you primarily need to care great care of, rather than the plants growing within it.
If you want to know more about bio diversity, or the organisms present in soil, there's some reading here
In regard to the addition of manure for aerobic (hot) composting, this is usually added as an 'inoculant', meaning it contributes organisms which help with the process.
In response to the edit you've made in your question, I'd query precisely what you mean by 'locally produced nitrogen', particularly since there's an implication in the latter part of the final sentence that this 'nitrogen' source could be one from inside your own property, as opposed to bringing in a 'nitrogen' source from outside. I suppose if you have horses, maybe cattle of some sort, you might consider composting their dung with straw for a year or so and using that instead of buying it in.
I would reiterate, though, that the use of composted animal manures on soil is not done primarily for nitrogen content anyway, as explained in the first paragraph of this answer.