Is it possible to allow sideloading and keep users safe?

> Are you allowed to run whatever computer program you want on the hardware you own?

Yes. It is a basic human right.

> This is a question where freedom, practicality, and reality all collide into a mess.

No; it isn't. The answer is clear and not messy. If you are not allowed to run programs of your choice, then it is not your hardware. Practicality and "reality" (whatever that means) are irrelevant issues here.

Maybe you prefer to use hardware that is not yours, but that is a different question.

That’s a great ideal, but Android is used both by sophisticated users who want a phone they can tinker with and the tech-illiterate grandparents of the world, who will never have a legitimate reason to install an app outside the Play Store, and who would never attempt to do that unless they were being guided by a scammer.