Maize has even been intentionally hyrbidized for almost a century; I'm less familiar with wheat from that sense.
Yes, tools like CRISPR are game changers and should be approached with caution (and we almost certainly aren't going to do so, at least for animal feed-stock crops), but GMO labeled food is very broad brush with often arbitrary distinctions (much like the "artificial" vs "natural" labeling rules)
But look at a picture of teosinte, and compare it to maize. Maize is emphatically not a natural plant; why should a plant grow appendages it's not strong enough to support? That shift in plant structure occurred over perhaps one or two millennia, and would have required extremely active selective breeding to occur.
Start poking at our plants' genomes, and the evidence for calling it genetic engineering is somewhat clearer. Our cereal crops basically suffer from plant equivalents to genetic conditions such as Down Syndrome. They shouldn't be able to survive, and indeed generally cannot survive without active management by humans. And being unable to survive without human intervention is common enough that we've given it a special name: domestication.
Scenario 1):
A random mutation decreases my yields. My community of 30 people can barely get by on the food we grow. Some of our children died from starvation and we are down to 28.
Scenario 2):
A random mutation increases my yields. My community of 30 people can easily get by on the food we grow. None of our children are dying and we expect 5 children to be born this year. I can sell the extra seeds at the farmer's market and make an additional profit.
Absolutely zero genetic engineering is needed to improve yields. This is just natural selection. Nobody has to be aware of the process for improvements to happen.
The next step would be to just buy the best seeds available at the farmers market. It would significantly more effective than natural selection but all you're doing is buying seeds from the farmer who is selling more food than everyone else.
Calling this engineering would be insulting to every other branch of engineering. Anyone buying food would be genetically engineering their food by this definition. Seriously, what other branch of engineering requires no knowledge of it happening?
By that same logic everyone is an economist. The laws of supply and demand happen even if you are not aware of them.
I'm tired of people diluting "professional" words into meaninglessness. It's not a colloquial term and it certainly shouldn't become one.
People would barter and buy seeds from farmers with higher yields with the intent of getting those larger yields themselves in future years. This is not natural selection.
I'm equally sick of people implying that ancient people were stupid and incapable of engineering.
As you mention fields, they are in fact an ancient invention to allow farming, and most importantly, an artificial invention. Nobody gets a full belly from the 3 plants in a window pot. One has to do large scale agriculture to feed large numbers of people, and this has been conducted for millenia. A field is at the very basis of agriculture. In order to make land arable, we've cut down forests, moved stones, drained swamps, leveled terrain, built irrigation systems, etc. Basically engineering work.
Fields do look like nature, but they don't represent nature. Wild type nature looks different.
TLDR: Humans are engineers. Always have been.
Not continent-spanning grow-labs, which is the proposition being forwarded.
2) Seed will be contaminated. It will taste as leaf or straw.