Re: "myth" of hives making their own queen
Daniel has it right. Queens in nature are planned on by the bees. The eggs are laid in pre-made cell cups and are planned and prepared for in advance by the bees.
A walk away split is totally UNnatural. No planning, eggs not laid in cell cups but are in regular worker cells, which prevents the developing queens from getting the full nourishment they would get if it was raised in a true queen cell from a pre-made cup.
Walk away splits will produce queens, but they will be not as well nourished when raised, so are inferior. Some say it does fine and gets good queens, but how long do those queens last? I've found, myself, that walkaway splits are only 50% successful if you follow the performance of the queens over time.
Make up a nuc to use as a cell builder, with a frame of eggs in it. Make it overly crowded with young nurse bees. 3 to 4 days later, remove all started queen cells and remove the frame of eggs, which are now larva, and insert another frame of eggs. This primes the bees to build cells as they are now in full production of royal jelly. Also, that last frame of eggs added, should be eggs laid in a virgin wax frame. This makes it much easier for the bees to remake the wax around the cells they choose to build into queen cells. Get this frame by inserting a frame of wax foundation into the center of the broodnest of your strong hive that you want daughters of the queen from. Check it daily, and as they start drawing out the wax, then make up your cell builder nuc. This will give you eggs in virgin wax to give the cell builder nuc.
20+ years, raise my own queens, feed when needed. I treat, but have not perfected varroa management yet.