If the apps sandboxed, how can installing an app cause breaches? As far as I know, iOS apps are sandboxed.

Either the sandbox is very weak and Apple instead relies on App Store audits, or they disallow users installing apps outside the app store to protect their 30% tax that makes them a LOT of money.

When you’re tricked into installing a nasty app, you’re likely also tricked into giving it whatever permissions it needs for the nastiness.

Which is not the fault of the OS

who's fault is it then, if not the OS? that's basically the os's job; to isolate and manage the system's resources and access to them therin

At the direction of the device owner, though.

the malicious app, even signed off the app store could also exploit unpublished vulnerabilities to gain elevated access and not require asking for permission. even or especially if it's not a full sandbox escape.

The sandboxes are regularly breached. Basically any time you hear about people "rooting" their phones, that's an intentional sandbox breach.

Not always. Unlocking the bootloader doesn't breach the sandbox since it factory resets the device.

Is that true? the process of sideloading and running a 3rd party app is pretty far from simple, trivial or even easy to explain to a grandma / child.

I think Apple will have to allow different stores in Europe soon. It'll be interesting to see what happens.