The variety angle is because 1) the more factors you can roll the dice on at any given moment, the more likely you can come up ‘winning’ with a magically terrible combo through mutation. That ocelot flu mutate to something that could infect bats? Groovy. No bats though, so doesn’t go anywhere. If you have bats though.....
2) Many animal viruses can be low or no impact in a species, and some can infect others to different effects. This gives a given virus more chances to roll the dice and get the ‘magic’ combo without killing itself off by killing the host. The more other species it gets exposed to; the better.
3) some species have elements more common with humans than others. If a virus gets mostly infectious in one host, adapting in another environment can get it closer to dangerous to humans.
Also, if you live in an area without solid electricity or reliable refrigerated trucks - what else are you supposed to do? If you grew up in one of those areas, why bother with the more expensive option if you’re used to this (or poor and don’t have a choice).
A lot of our simplification in diet now is due to the ability to choose higher grade options coupled with strict government regulations on how food sold to the public can be sourced and the conditions it can be ‘made’ in. It used to be (several generations ago now), wild hunted deer, pidgeons, squirrel, a side of pork from your neighbor, etc. were common parts of daily food intake, and you HAD to cook your food or you wouldn’t go a week without something really nasty happening to you. There are many parts of the county that still do this, though usually more out of convenience than necessity.
Now you can pick from animals raised for purpose, with supply chains inspected and complying with a books worth of regulations. In many cases, you could go years without getting sick if you didn’t cook your food (don’t try this, it’s still a dumb idea).
It’s easy to point fingers, but if you haven’t seen it and lived in the environment, you can’t just change it without a lot of other things happening first or very nasty side effects (starvation, nutritional issues, etc).