I used to be concerned with a 'curing' phase after the thermophillic stage when I do hot composting, but now I don't bother. I apply it right after the hot phase without worry. The main case, as I understand it, for curing is to reduce phytotoxicity. Phytotoxicity occurs when certain compounds are still present after the hot phase. Some of these compounds may take time to break down and not necessarily heat. But if you are using common materials like weeds, leaves, grass clippings, foodscraps, and livestock manure; and you don't regularly apply pesticides or use non-organic
feed with your livestock. These compounds causing phytotoxicity should be a non-issue.
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/phytotoxicity
Regarding nutrient leaching. This could be a problem with your soil if it has a reduced cation exchange capacity. If your soil is high in organic matter, your cation exchange capacity should be fine to handle nutrients breaking down from a hot compost. If your soil is low in organic matter, you could use
biochar to increase your cation exchange capacity.
On our farm, we like to use hot compost to apply after crops are harvested because those veg beds usually need more nutrients immediately. We 'mostly' use cold 'cured' compost the beginning and end of season, or for a midway
boost for long term crops like cabbage. But I've used hot compost on our beds midway through a crop's growth stage with no problems. So we're not really sticklers, we just use what we have. If you have healthy soil with a diverse soil biology, it should be able to handle 'uncured' compost that has gone through the thermophilic phase.
Hope that helps!