Because you can't always get what you want, and unless Apple is a monopoly (they aren't) or causing actual harm (they aren't) they shouldn't be forced to give you something just because you'd like to have it.
I mean heck, I'd LIKE to have a single gaming console where I can play all my games from all the systems I've ever owned. That doesn't mean Nintendo or Sony or Microsoft should be forced to make it. I'd also LIKE to have every game ever made available for $1 each. Again, why should someone be forced to do or give me something just because I want it?
Setting that aside, allowing for side loading, even as an option, creates a security holes. Your wife's Android device, even without side loading enabled is less secure than an iPhone where it can't be enabled. This is an objective fact. There is a question about how much less secure, maybe its only a tiny amount, but it is inherently less secure because it has a greater attack surface. And yes, in your wife's case it might be fine, she might not be in a position where she needs to access Apps from side loading or 3rd party stores. But she is a single data point, one that serves to prove only that an individual case can exist NOT that an overall trend is likely or true. While she may not be in a position where she has to side load apps, not all users would be in that position due to various circumstances. As soon as side loading and/or alternate App Stores are a possibility, it means the likelihood of one or more key apps going that route goes up significantly.
Further, we already know there are multiple developers who want to get out of the Apple App Store model with its various privacy and security related restrictions. Facebook for one, Amazon probably as well. Google for sure would LOVE to be able to get more data on users. The API's and OS can enforce this to some degree, but the AppStore is the final barrier. An App introduced outside that model can use undocumented API's and other tricks to bypass at least some restrictions, and attempting to lock those down means Apple has to devote resources to other areas, areas it does not currently have to because the AppStore review process can prevent it. It also breaks the ultimate backstop against bad apps, Apples ability to completely revoke the apps certificate. Apps installed outside the AppStore would not be subject to this limitation. A bad app side loaded or installed via the Epic store or whatever would be able to continue operating and if Apple wanted to implement a further level of protection it, again, would require significant dedication of resources to try and find an alternative.
What we have now is like the difference between living in a city (Android) and living in the country (iOS). A person can choose to live in either one, some prefer one, some prefer the other, some have no strong preference either way and will go wherever life takes them. The people trying to force Apple to change are like people trying to turn a country town into the big city. What they SHOULD do is just move to the city (i.e. buy an Android) if thats so important to them. Instead they are trying to change the country town. "But you'll have more choices if it becomes like the city!" they say. "And if you don't like the choices you don't have to use them, you can still keep things the same!" they say. Except thats not true. The town will have changed, it will lose the advantages it had, the things people who wanted to live there CHOSE to live there for (or chose the iPhone fore). It will become more and more like the city, until instead of a city and a town, there are just two slightly different cities and no town. The choice will have been removed.
Right now you have a choice, if you want side loading and alternate app stores, you can buy an Android device. There are many many MANY options. No one is stopping you. Its really quite easy. I get that you may not like some aspects of the Android experience, you may prefer some of the things Apple does. I get that you want the best of both worlds, thats absolutely understandable. But just because you want that doesn't mean someone has to give it to you. As in most things in life, you have to weigh the pluses and minuses of each option and pick the one that best suits you. Not force someone to make the one you want.