It appears that humans (and at least some other primates) easily learn fear of some animals, such as snakes and spiders, and can easily learn fear of cockroaches, due to their sudden appearance and rapid movement. Being surprised and startled by cockroaches can lead to fear of cockroaches, which can result in disgust and loathing. Our perception of cockroaches as living in garbage and filth aids that disgust and loathing. The "attar of roaches", the distinctive and unpleasant aroma produced by some species doesn't help humans like them. Thus, dislike and disgust are common modern responses to cockroaches.
However, these are not universal responses (just as they aren't universal responses to snakes and spiders).
There is a broad spectrum of attitudes to cockroaches. Apart from the disgust and loathing you note in your question, there is non-disgusted dislike of them as an annoying household pest. There has been treatment of them (e.g., in parts of Russia and Eastern Europe) as benevolent and useful inhabitants of the household, bringing wealth and prosperity. Sometimes this was specifically due to cockroaches increasing the fertility of one's livestock. When moving to a new house, efforts would be made to move as many of the cockroaches as possible from the old house to the new. (In some parts of Croatia, snakes had a similar beneficious and protective reputation.) This type of attitude might only apply to some species of cockroaches (e.g., black cockroaches) while others (e.g., brown cockroaches) were regarded as annoying pests.
In some places, cockroaches have a long history of being food for humans. Two notable places where they are eaten today, following long tradition, are Mexico and Thailand. They are farmed for food in China, but the most Chinese cockroach farming is aimed at their use in medicine, and culinary use is a minor part of the industry. Cockroaches don't have a good image in China, so the farmers don't widely advertise what they are raising. Sometimes, incidents such as as the escape of about 1 million cockroaches from one farm attract some media interest. (How many farmers can tell stories of how 1 million of their livestock escaped in one day?) For a quick look at Chinese cockroach farming, see:
Further reading:
Marion Copeland, Cockroach, Reaktion, 2004.
Marjanić, Suzana. (2019). "Cockroaches: From Belief Narratives to the Contemporary Visual Practice of Catherine Chalmers, or How Cockroaches Have Survived on Earth for More than 320 Million Years". Folklore: Electronic Journal of Folklore. 77. 139-158. https://doi.org/10.7592/FEJF2019.77.marjanic