There are a few reasons for not feeding cooked foods to worms (Eisenia spp.) in a smaller household size worm farm. It's not because the food is cooked but what it often contains.
The earthworm used in vermiculture is usually Eisenia fetida (red wigglers) though other Eisenia species are sometimes used. All Eisenia are epigeic species meaning they live in the junction of decomposing organic matter (such as leaf litter, aging manure, rotted fallen trees) and their natural food is decaying plant matter and bacteria that are also digesting the organic matter. They don't make use of small dead animals (meat and fat).
In large scale commercial vermiculture operations, leftover and past-due-date foods from restaurants, institutions, nursing homes and schools are used along with plant matter and carboard and paper. I'm not sure how they balance cooked foods but possibly much less is used than plant matter.
The fact food is cooked isn't the problem but what's in it and/or what happens to it when added to the bin. If you have leftover vegetables and fruit that's been cooked with no added salt, it's perfectly acceptable. A certain amount of sweetened cooked fruit is also fine as the worms will eat that too. But ready-made foods usually have preservatives, salt, fats and spices added. Either worms won't eat it, leading to odour caused by mouldy rotten food, or it can make them unthrifty and even killing off your worms if it's fed them repeatedly.
Fats and meat along with cheeses and dairy products will also not be eaten so shouldn't be used. Sites about vermiculture say onions and garlic can 'burn' the worms skin which is the problem with citrus fruit. They can be used but in very small amounts and should be mixed well with their other food.
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