When composting isn't an option—alternatives

We can only compost so much stuff at a time, and some things we don't want to compost, due to pathogens or whatever. So, I got an idea: Why not just burn it, and use it as ash in the garden? Works great so far. We already use a wood stove to burn wood into ash for the garden. Our compost thing is pretty much full, and it's winter. So, I've been throwing banana peels, an apple, carrot scraps, moldy tomatoes, and even eggshells on the fire with our wood that warms the house. It works. They burn into ash. No more waste. It should make for a somewhat less alkaline ash, this year.

So, I got to thinking, why don't people burn manure and stuff like that into ash more often? It would probably be nice for the garden, and it wouldn't be so high in calcium as wood ash; there wouldn't be weed seeds, either, and it could be used similarly to water soluble fertilizer. (Ash mixes with water pretty decently, whether or not it's scientifically water soluble.)

I imagine one could incinerate human feces (thus disinfecting it). They have special incinerating toilets. I wonder how nice that ash would be for the garden. Of course, you'd want to limit your sodium chloride intake (since plants only need so much sodium chloride; about 90% of that is extreted via urine, says Google, quoting wiley.com), and only use medication-free excrement. Poop ash would be a great way to retain sustainable nutrients for the garden (and even add to the existing nutrient base, since we buy food, too). The nitrogen loss isn't a big concern (especially as soil bacteria can build it up). It's more the potassium/zinc/copper/iron/magnesium/phosphorus that I'm concerned about; those should remain in the ash.