All transformers are some combination of hand and machine wound. I doubt anyone holds a bobbin on one hand and wraps wire around it. There are many examples on YouTube, both good and bad.
As to computer winding: the computer in most winders simply controls the pitch of the wind and counts the turns. Tensioning is done on the spool de-reeler. There is a lot to setting up the winder, insulating the layers, bringing out the wires. When I wind I know what effects what because I designed the transformer. When I show someone else I can stress the important things, however it is a lot to learn. Why are some bakers, chefs and other artists better than others? Even if they show someone all they have done, the end result is rarely the same.
One can wind very nice transformers with very simple home-made winders. I hope to offer transformer winding/construction as one of my classes here in Berkeley. There is no reason for not making your own transformers if you really want to. It's not rocket science, just something to learn from someone else who figured it out. It does take some effort to gather the materials, learn the design techniques. That part I would provide.
BTW, I have measured a Heyboer output transformer, sadly it was not so good. Edcor is inexpensive but not well thought of. Hammond may be better but I have not tested their wares. Winding with silver strikes me as silly for a few percent better conductivity and the fine wire primary is rarely silver as it is too soft to make thin wire. I know the Dynaco, Acrosound and many transformers made around the height of home building were very good. The guys making stuff these days have not done their homework. Besides designing transformers I have developed a battery of bench tests to determine their performance before they go into an amp. Since the transformer is an important part of the feedback loop it's characteristics must be known separately.