Your instincts are incorrect - at least in a rural, or semi rural setting.
Your chickens may be very safe and easy to raise in an urban environment that is free of small and medium sized predators, but outside of that environment there are many, many things that will very quickly dispose of all of your chickens - sometimes in just one night.
Raccoons, weasels, foxes, coyotes, large birds (vultures, hawks, owls), bobcats ...
In our rural area (west marin county, california) we need to be on our A game to keep the chickens alive ... raccoon traps set, elevated coop, hens locked up nightly, wings clipped so they can't get out of the run, high fence, three hot electric wires, etc., etc.
A cow on the other hand is too big for most of those animals (a hawk can't carry away a calf) and the mother (and other mothers) are nearby. They're big.
If you get it wet, you'll burn your barn down because it composts.
It's like having a dog vs. a cat as a pet. A cat just needs to be fed and given a box where they can place their waste. A dog needs to be walked, socialized with other dogs, etc. Do you need to travel for a 2-day weekend? With a cat, while not ideal, you can get away with leaving behind plenty of food and water along with an extra litter box. You simply cannot abandon a dog on its own for 2 days.