Do restaurants not have the “no outside food/drink allowed” stickers on the doors where you live?

After I leave the McDonalds "store" with a Big Mac, I can have their food with outside food/drinks. After I leave the Apple Store with an iPhone, I cannot use my phone with outside apps.

If you tried to bring in your own burger condiments, I don't think it's likely that McDonalds management would agree to put them on for you.

But people are not asking Apple to install their apps for them on their own iPhone. People are only asking Apple to stop preventing them from installing apps. After you pay for the iPhone, it is yours, after you leave the physical Apple Store you are not in their store any more.

If McDonalds sent someone to my house with me after I purchase a Big Mac, and tried to stop me when I wanted to put some of my own condiments in it, I would find this creepy and controlling behavior very weird.

That still doesn't make Apple a monopoly.

Apple is the only place you can buy an iPhone, yes, but you don't have to buy an iPhone. You can buy an Android phone instead (in fact Android has about 2/3 of the market worldwide, which, condiments aside, make the claim that Apple is a "monopoly" pretty dubious).